Here is a triangular pyramid and its net.
The lateral faces are congruent triangles. The base (shaded) is an equilateral triangle.
(All lengths are in millimeters.)
Answers
Answer:
a) Area of the base of the pyramid = [tex]15.6\ mm^{2}[/tex]
b) Area of one lateral face = [tex]24\ mm^{2}[/tex]
c) Lateral Surface Area = [tex]72\ mm^{2}[/tex]
d) Total Surface Area = [tex]87.6\ mm^{2}[/tex]
Step-by-step explanation:
We are given the following dimensions of the triangular pyramid:
Side of triangular base = 6mm
Height of triangular base = 5.2mm
Base of lateral face (triangular) = 6mm
Height of lateral face (triangular) = 8mm
a) To find Area of base of pyramid:
We know that it is a triangular pyramid and the base is a equilateral triangle. [tex]\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\[/tex]
[tex]{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}[/tex]
b) To find area of one lateral surface:
Base = 6mm
Height = 8mm
Using equation (1) to find the area:
[tex]\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}[/tex]
c) To find the lateral surface area:
We know that there are 3 lateral surfaces with equal height and equal base.
Hence, their areas will also be same. So,
[tex]\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}[/tex]
d) To find total surface area:
Total Surface area of the given triangular pyramid will be equal to Lateral Surface Area + Area of base
[tex]\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}[/tex]
Hence,
a) Area of the base of the pyramid = [tex]15.6\ mm^{2}[/tex]
b) Area of one lateral face = [tex]24\ mm^{2}[/tex]
c) Lateral Surface Area = [tex]72\ mm^{2}[/tex]
d) Total Surface Area = [tex]87.6\ mm^{2}[/tex]
Answer:
Sample answer A triangular pyramid with an equilateral triangle for a base has four faces the equilateral triangular base and
three congruent isosceles triangular faces
Step-by-step explanation:
Related Questions
A triangle has side lengths 4 cm, 4 cm, and 7.5 cm. The angle measures are 20°, 20°, and 140°. What type of triangle is this triangle? acute isosceles acute scalene obtuse scalene obtuse isosceles
Answers
Because two side lengths are identical it is an isosceles triangle and also at least one angle is less than 90 degrees so the answer would be an acute isosceles triangle.
Answer:
acute isosceles.
Step-by-step explanation:
Simplify the following expression
x^5/x^-2=x^n
A. 8
B. 2
C. 7
D. 10
Answers
Answer:
7
Step-by-step explanation:
x^5/x^-2=x^n
x^5=x^n×x^-2
x^5=x^-2+n
5=-2=n
n=7
this is 100% correct
plzz mark me brainliest
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
(m^2 + -2m + -1) (5m^4)
Answers
Answer:
[tex]5m^6 - 10m^5 - 5m^4[/tex]
Step-by-step explanation:
All you need to do is distribute the [tex]5m^4[/tex] to ([tex]m^2-2m - 1[/tex]), like so:
([tex]m^2-2m - 1[/tex])[tex](5m^4)[/tex]
[tex]5m^6 - 10m^5 - 5m^4[/tex]
Find the value of x and y. Will mark brainliest.
Answers
Answer:
y=3, x=5
Step-by-step explanation:
18=6y, so divide both sides by 6 to get 3=y.
45=9x, so divide both sides by 9 to get x=5.
Answer:
x=5 y =3
Step-by-step explanation:
Opposite interrior angles have the same Number of degrees. So 9x=45. X has to be 5. y = 3 because 3 times 6 is 18. Which is the same number as the opposite vertical side.
help please asap :)))
Answers
Answer:
Step-by-step explanation:
The volume is calculated like:
V= length* hauteur* wide
V= 5* 2 3/4* 10 1/2
[tex]V= 5*\frac{11}{4} *\frac{21}{2} =\frac{5*11*21}{4*2} =\frac{1155}{8}=144.375 \\=144 \frac{3}{8} in^{3}[/tex]
please help me with this it is the last quastion i need help with
Answers
Answer:
$92.92
Step-by-step explanation:
$72.60 * 20% = 14.53
$72.60 + 8%= $78.40
$78.40 + $14.52 = $92.93
20% of 72.60 (or 72.60 x .20) is 14.52.
72.60 + 14.52 = 87.12
what are the zeros of (3x−2)(x+4)
Answers
Answer:
x = 2/3 x = -4
Step-by-step explanation:
(3x−2)(x+4)
Set this equal to zero
(3x−2)(x+4) = 0
Using the zero product property
(3x−2) =0 (x+4)=0
And solve for x
3x =2 x = -4
x = 2/3 x = -4
please answer this i’ll give you 15 points
Answers
Answer:
B
Step-by-step explanation:
you round 33 to 30 and 87 to 90
Answer:
Well I think it's B.. Sorry for the late answer.
Step-by-step explanation:
Find the area. Will mark brainiest.
Answers
Answer:
9)Area=64in²
10)Ms.Surruco's classroom
...........................
HURRY PLEASE!! WILL MARK THE BRAINLIEST
Which of the following are factors of the
polynomial?
Answers
Answer:
All of the above
Step-by-step explanation:
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Since, they all have a degree of 1 they are all polynomials.
What is the area of the rhombus? Please help!
Answers
Answer:
Step-by-step explanation:
1200
Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeters, as shown.
A right triangle with side lengths 60 centimeters, h, and hypotenuse 63 centimeters.
In centimeters, what is the approximate height of the ramp? Round the answer to the nearest tenth of a centimeter.
Answers
Answer:
Answer is 19.2
Step-by-step explanation:
60x60= 3600 63x63= 3969
3969
- 3600 = 369 square root of the 369= is 19.2
The approximate height of the ramp is 19.2
Given: Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeters, as shown.
A right triangle with side lengths 60 centimeters, h, and hypotenuse 63 centimeters.
How to determine in centimeters, what is the approximate height of the ramp?
The area will be 60x60= 3600
=> 63x63= 3969.
Thus height is 3969- 3600 = 369 and the square root of the 369
=19.2
Learn more about triangles on: https://brainly.com/question/16439676
#SPJ2
Adam's goal is to practice piano for 200 minutes every week. Which practice schedule would allow him to meet his goal?
20 minutes per night, 7 days per week
30 minutes per night, 6 days per week
40 minutes per night, 5 days per week
50 minutes per night, 3 days per week
Mark this and return
Save and Exit
Answers
Answer:
40 minutes per night, 5 days per week
Step-by-step explanation:
Tamanika got a raise in her hourly pay, from $15.50 to $17.36. Find the percent increase
Answers
Answer:
12%
Step-by-step explanation:
The required percent increase is 12%
Tamanika got a raise in her hourly pay, from $15.50 to $17.36
What is percentage?percentage is defined as, composition of something out of whole inbounds of 100.
since = 17.36 - 15.50/15.50 x 100
= 1.86/15.50 x 100
= 0.12 x 100
= 12
Thus the required percent increase is 12%.
Learn more about percent here:
https://brainly.com/question/14699403
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Mindi planted beans in 4/10 of her garden and peas in 5/10 of her garden. What fraction of the garden has beans or peas?
Answers
What is this number in standard form?
(7×100)+(4×1100)+(8×11,000)
Answers
Answer:
Step-by-step explanation:
factor out 100
100[7 + (4 * 11) + (8 * 110)]
100[7 + 44 + 880]
100 (931)
= 93100
standard form is 9.31 * 10^4
The standard form for the number (7×100)+(4×1100)+(8×11,000) is, 9.31×10⁴
What is the standard form of a number?The standard form for a number is a method by which we write number in a format like b×10ˣ. The value of b should be in between 0 to 10.
Given Number,
⇒ (7×100)+(4×1100)+(8×11,000)
by taking 100 common from all the three terms,
⇒ 100[ 7+ (4×11) + (8×110) ]
⇒ 100[7+44+880]
⇒ 100×931
⇒ 9.31×10⁴
Hence, The number can be written as, 1.39×10⁴
To know more about Standard from check:
https://brainly.com/question/13139379
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What is the most appropriate level of accurarcy for measuring the height of a tree
Answers
Answer:
meters because trees can be tall.
Write a problem that could be modeled with y=200(0.9).
Answers
First, I need to decide what equation this is like.
I believe this is y=mx.
We know that x is typically the input, and m is the constant function.
Y is the output.
So the original function may have been y=200x.
The only difference is now we've been given something to apply to the equation, in place of x.
2. Imagine a cloning machine. Whatever you put in, you get a copy of, and the original thing you put in. Its function would be y=2x. Let's pretend we decided to put three things in; 3 would go where x is.
Y would be the result of 3 copies and their originals, or 2(3).
(6=2(3))
Now, when someone else decides to use the cloning machine, they may put any number in, but the only properties that will change are y and x, not m.
The function will remain y = 2x. Any number could go in place of x, and multiplying x by 2 will give you the y. As long as you have a different value for x, the y will never be the same.
3. So now we have an understanding of what it means, we see that we have been given an x value to insert; an input.
A more practical example could be someting with money. This won't be entirely realistic, because we are dealing with a fraction of a number and another large number.
4. I decided to go with flour. I wanted the 200 to represent pennies, or cents. Before I landed on this, I looked up the cost of flour per pound. I found that the average is .43 dollars, which isn't terribly close to two dollars. But maybe the flour is high quality, so we can stick with that.
5. Seeing that this equation, y=200x, means we are charging 200 cents, or two dollars, we can write a problem from here.
Sylvia is in charge of selling home-harvested flour from an organic farm. She charges two dollars per pound of flower. Today, her next-door neighbors hope to buy a ninth of pound of flour, and they insist on paying with pennies. How many pennies do they need to pay for their order?
Let me know if this helped, or if you have any questions!
What is the area of the following right triangle?
Answers
Answer:
30 square units
Step-by-step explanation:
The area of the given right triangle can be found a couple of ways:
Pythagorean theoremThe missing side length can be found using the Pythagorean theorem relation between the sides:
c² = a² +b²
13² = a² +5²
a² = 169 -25 = 144
a = √144 = 12
Then the area is ...
A = 1/2ab = 1/2(12)(5) = 30 . . . square units
__
TrigonometryThe angle at lower right can be found from the trig relation ...
Cos = Adjacent/Hypotenuse
cos(A) = 5/13
A = arccos(5/13) ≈ 67.38°
The area can be found from these side lengths and the angle:
A = 1/2bc·sin(A)
A = 1/2(5)(13)sin(67.38°) = 30 . . . square units
_____
Additional comment
The sine of the angle can be computed from the cosine using the identity ...
sin(x) = √(1 -cos²(x))
In this case, the sine of the angle would be found to be 12/13, so the area would be computed as ...
A = 1/2(5)(13)(12/13) = 1/2(12)(5) . . . . same as using the Pythagorean theorem
will give brainlist if right
Answers
Answer:
10/50 = 20%
20% experimental probability
1/5 experimental probability
The area of a rectangle is 99 square inches. What is the new area of the rectangle if the height were five times long and the base decreased by one-third? Answer_square inches
Answers
Answer:
330 square inches
Step-by-step explanation:
99 x 5 =495
495 x 2/3 =330
What is the height of the pole?
top
O 12 ft
O 125 ft
O 18 ft
O 182 ft
Answers
Hope this helps
Can anyone help me out with number one?
Answers
Answer:
[tex]232 cm^{2}[/tex] (B.)
Step-by-step explanation:
Don't overwhelm yourself. Take a deep breath and look at the triangle that has the height of 14 cm.
Recall that the area of a triangle is A= 1/2bh
The base of the triangle is 8 cm, if you eyeball it with the square. The height is given as 14.
1/2 (14)(8)
= 56 cm^2 x 2
= 112 cm^2
Great! We found two of the triangles (there are two of these, look at the paper)
Now let's take a look at the second triangle with the height of 12 cm.
Eyeball the base, which is 6 cm from the square in the middle.
1/2 (6)(12)
= 36 x 2
= 72 cm^2 (there are two of these triangles)
The easy part comes. The area of a square is simply
A= bh
= (6)(8)
= 48 cm^2.
ADD 'EM UP
48 + 72 + 112
= 232 cm^2
Answer:
B) 232
Step-by-step explanation:
Do 14 x 8 to find the top and bottom triangle. 112. Then do 12 x 6 to find the left and right triangle. 72. The find the area of the rectangle 6 x 8 = 48. Add up all the answers. 112 + 72 + 48 = 232 is the answer.
How many outcomes are in the sample space of flipping a coin in spinning a spinner with sections labeled 1-4
Answers
Answer:
8 outcomes
Step-by-step explanation:
A coin has two possible outcomes: heads or tails.
The spinner has four possible outcomes: 1, 2, 3 or 4.
If we combine then, the number of outcomes will be the product of their number of outcomes:
2 * 4 = 8
So we will have a total of 8 outcomes:
heads, 1 / heads, 2 / heads, 3 / heads, 4 /
tails, 1 / tails, 2 / tails, 3 / tails, 4
Probability
Consider the following set of numbers:
{1,2,3,4,5,6,7,8,9,10)
What is the probability of drawing an odd number or a
multiple of 3?
9/10
1/2
7/100
3/5?
Answers
Answer:
1/2
Step-by-step explanation:
Can anyone please help me here in this proplem
Answers
Answer:
270Step-by-step explanation:
I DID THE TESTAnswer: 270
Step-by-step explanation: First find the volume to the figure and find the volume of the unshaded part and subtract . Hope this helps 8-)"
5 ft
A
13 ft
a.
sin A=7
islam
/
A= 12,
A = 12 sec A
-
12
cos A = 132
n la
12
COS A = 13
CP
5, CSC A =
b.
sin A = , tan A = o, sec A = 1
12
sin A = 13, tan A =
12
5, sec A =
13
12
COS A = 5, cot A = 5, CSC A =
al
5
COS A = 13, cot A = 12, CSC A -
Answers
Answer:
i don't understand what the question is please explain what the question is.
When you graduate from high school, you deposit all of your graduation cash into an account earning 5% interest. Ten years from now you will have
$5000 in that account. How much money did you deposit?
Answers
Solve this brain teaser, please!!!
Answers
Answer:
0 in the end they all burn out
Step-by-step explanation:
Answer: 10
Step-by-step explanation:
The cylinder shown has a volume of 30 cubic units.The come and the cylinder have the same height and the same base.What is the volume of the cone?
Answers
Answer:
The volume of the cone is 10 cubic units
Step-by-step explanation:
Given
Solid Shapes: Cone and Cylinder
Volume of Cylinder = 30 cubic units
Required
Volume of Cone
From the question; we have that the cylinder and the cone has the same height (h) and the same base;
Since they have the same base, then this means they have the same radius.
The Volume (V) of a cylinder is calculated as follows
[tex]V = \pi r^2h[/tex]
Substitute 30 for V
[tex]30 = \pi r^2h[/tex]
The Volume (Vc) of a cylinder is calculated as follows
[tex]V_c = \frac{1}{3} \pi r^2h[/tex]
From the volume of a cone, we have that [tex]\pi r^2h = 30[/tex]; This means that we can substitute 30 for [tex]\pi r^2h[/tex]
[tex]V_c = \frac{1}{3} \pi r^2h[/tex] becomes
[tex]V_c = \frac{1}{3} * 30[/tex]
[tex]V_c = 10[/tex]
Hence, the volume of the cone is 10 cubic units
