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

Answer:

A) 106 ft^2

Step-by-step 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

$Area=\frac{1}{2}\base \times height$

$Area=\frac{1}{2}\times 6\times 5.2$

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

The area of the three lateral face is

$Area=3\times \frac{1}{2}\times 6\times 10=90ft^2$

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

Answer 2

Answer:

106 ft²

Step-by-step explanation:

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

$SA = \frac{H B}{2} + \frac{3 B S}{2}$

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:

$SA = \frac{5.2 * 6}{2} + \frac{3 * 6 * 10}{2} = 15.6 + 90 = 105.6$

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