Question

Find the surface area of the regular pyramid shown to the nearest whole number.

A picture of a five-sided pyramid with height 16 m, side is 10 m and width from center point of base pentagon to side is start root 3 end root. Label: Not drawn to scale.
(1 point)
Responses

740 m2
740 m 2

480 m2
480 m 2

1,480 m2
1,480 m 2

715 m2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a pyramid, we need to find the sum of the areas of the base and the five triangular faces.

First, let's find the area of the base pentagon:
The area of a regular pentagon can be found using the formula: area = 1/4 * sqrt(5(5 + 2sqrt(5))) * s^2, where s is the side length of the pentagon.
In this case, s = 10 m.
Plugging in the values, we get:
area = 1/4 * sqrt(5(5 + 2sqrt(5))) * (10)^2
area ≈ 172.05 m^2

Next, let's find the area of one of the triangular faces:
The area of a triangle can be found using the formula: area = 1/2 * base * height.
In this case, the base of the triangle is 10 m and the height is 16 m.
Plugging in the values, we get:
area = 1/2 * 10 * 16
area = 80 m^2

Since there are five identical triangular faces, the total area of all the faces is 5 * 80 = 400 m^2.

Therefore, the total surface area of the pyramid is the sum of the base and the triangular faces: 172.05 + 400 = 572.05 ≈ 572 m^2.

So, the nearest whole number surface area of the regular pyramid is 572 m^2.

The options provided do not include this answer, so none of the options are correct.