Question

Need to know the answer for this question.

Answer 1

The total surface area of the square-based pyramid is 64 square inches.

Explanation:

The net of a solid shape refers to a 2D representation of the shape when it is flattened out into a plane.

The net of the given square-based pyramid consists of:

• A square (the base) with side lengths measuring 4 inches.
• Four congruent triangles, each attached to one of the sides of the square, with base 4 inches and height 6 inches.

(Please refer to the attachment for the drawing of the net of the given pyramid).

The formula for the area of a square is A = s², where s is the side length.

The formula for the area of a triangle is A = (1/2)bh, where b is the base and h is the height.

Therefore, the formula for the total surface area of the given square-based pyramid is:

`\sf Total\;S.A.&=s^2+4 \cdot (1)/(2)bh`

Given s = 4, b = 4 and h = 6, substitute these values into the formula and solve for S.A.:

`\begin{aligned}\sf Tota\;S.A.&=\sf s^2+4 \cdot (1)/(2)bh\\\\&=\sf 4^2+4 \cdot (1)/(2) \cdot 4 \cdot 6\\\\&= \sf 16+2 \cdot 4 \cdot 6\\\\&=\sf 16+8 \cdot 6\\\\&= \sf 16+48\\\\&=\sf 64 \; in^2\end{aligned}`

Therefore, the total surface area of the square-based pyramid is 64 square inches.