Question

Use the net as an aid to compute the surface area (rounded to the nearest integer) ofvthe triangular pyramid with an equilateral triangle base. A) 106 ft^2 B) 114ft ^2 C) 122ft^2 D) 130ft^2

Answer 1

A) 106 ft^2

Explanation:

The total surface area is the area of the base triangular face and the three lateral faces.

The base triangular face has length of its base to be b=6 ft.

The height of this triangle is 5.2 ft.

The area of this triangle is

`Area=(1)/(2)\base * height`

`Area=(1)/(2)* 6* 5.2`

`Area=15.6ft^2=16ft^2` to the nearest integer

The area of the three lateral face is

`Area=3* (1)/(2)* 6* 10=90ft^2`

The total surface area is therefore 90+16=106 square feet

Answer 2

106 ft²

Explanation:

The surface area of a triangular pyramid is calculated with the following formula:

`SA = (H B)/(2) + (3 B S)/(2)`

Where:

H is the height of the triangle base,

B is the side of the base triangle

S is the length of the slant.

so, if we plug in our numbers, we have:

`SA = (5.2 * 6)/(2) + (3 * 6 * 10)/(2) = 15.6 + 90 = 105.6`

105.6 sq ft, which we round up to 106 square feet.