Question

Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral triangle base.

A) 224 m2
B) 240 m2
C) 254 m2
D) 270 m2

Answer 1

Correct answer is
`C)\ 254\ m^(2)`

Explanation:

As per the given diagram, we know the following details:

Height of the triangular pyramid is 14m.

Side of base = 10m

Height of Triangular base = 8.7m

Formula for surface area of triangular pyramid:

`\text{Area = Area of Triangular base + 3 }*\text{Area of side triangle}`

(Triangular base is shown in the dotted lines in the question figure.

The other 3 triangles are the side triangles.)

We know that,

`\text{Area of a triangle = }(1)/(2) * \text{Base} * \text{Height}`

`\Rightarrow \text{Required Surface Area = } (1)/(2) * 8.7 * 10 + 3 * (1)/(2) * 14 * 10\\\Rightarrow (1)/(2)* (87 + 3 * 140)\\\Rightarrow (1)/(2)* (87 + 420)\\\Rightarrow (1)/(2) * 507\\$\approx$ 254 m^(2)`

Hence correct answer is
`C)\ 254\ m^(2)`.