ANSWER THESE TWO QUESTIONS FOR ME:

1. If the surface area of a cube is 390 cm², then which best describes the length of the side of the cube?

A. less than 7 cm
B. between 7 cm and 8 cm
C. between 8 cm and 9 cm
D. greater than 9 cm

2. The net below shows equilateral triangles. What is the total surface area of the triangular pyramid in square feet?

Answer:

65^2

Step-by-step explanation:

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#1:

Between 8 cm and 9 cm

Work:

SA = 6s^2  

390 = 6 s^2

390/6 = 6s^2 /6

65 = s^2

sqrt(65) = s

s = 8.06

#2:

The total surface area of the triangular pyramid is 107 * square feet.

What is a triangular pyramid?

Take a triangle. This is a base. Now take 3 triangles such that each of them are connected to one-one side of the first triangle and when they're taken together, they form a closed object, called as a triangular pyramid.

We are given that;

The length of median from outer triangle to side of the inner triangle is 8 ft

Side of inner equilateral triangle is 12 ft

Now,

First, we can find the height of the outer equilateral triangle using the Pythagorean theorem:

a is half the length of the side of the inner triangle (6 ft), m is the length of the median (8 ft), and b is the length of the side of the outer triangle (unknown).

a^2 + (m/2)^2 = b^2

b^2 = 6^2 + 8^2/4

b^2 = 36 + 4

b^2 = 40

b = sqrt(40)

b = 2 * sqrt(10)

So the height of the outer triangle is:

h = b * sqrt(3)/2

h = sqrt(30)

Now we can find the area of each equilateral triangle using the formula:

A = (sqrt(3)/4) * s^2

For the inner triangle:

A_inner = (sqrt(3)/4) * 12^2

A_inner = 36 * sqrt(3)

For the outer triangle:

Now we can find the area of the base, which is just the area of the inner equilateral triangle:

A_base = A_inner

A_base = 36 *

Finally, we can find the surface area of the triangular pyramid by adding the areas of the four triangles and the base:

SA = A_inner + 3 * A_outer + A_base

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