Question

Help me find surface area of a net, look at the image.

Answer 1

`\textsf{C)}\quad (5)/(16)\; \sf yd^2`

Explanation:

The net of a square-based pyramid is made up of:

• One square base.
• Four congruent triangular faces.

From inspection of the given net:

• Side length of the square base, s = 1/4 yd.
• Base of a triangular face, b = 1/4 yd.
• Height of a triangular face, h = 1/2 yd.

The area of a square is the square of one of its side lengths.

The area of a triangle is half the product of its base and height.

The total surface area of the pyramid is the sum of the area of the square base and the area of 4 congruent triangles.

Therefore:

`\begin{aligned}\sf Total\;surface\;area&=\sf Area_(square)+4 \cdot Area_(triangle)\\\\&=s^2+4 \cdot (1)/(2)bh\\\\&=\left((1)/(4)\right)^2+4 \cdot (1)/(2) \cdot (1)/(4) \cdot (1)/(2)\\\\&=(1^2)/(4^2)+(4 \cdot 1 \cdot 1 \cdot 1)/(2 \cdot 4 \cdot 2)\\\\&=(1)/(16)+(4)/(16)\\\\&=(1+4)/(16)\\\\&=(5)/(16)\; \sf yd^2\end{aligned}`

Therefore, the surface area of the pyramid is 5/16 yd².