Question

the following figure is a net of a pyramid. each value below is in inches.
what is the surface area of the pyramid?

Explanation:

Step1: Identify base and triangular faces

The net has a square base (side length $5$ inches) and 4 triangular faces: 2 triangles with base $5$ in, height $16$ in; 2 triangles with base $5$ in, height $10$ in.

Step2: Calculate base area

Area of square base: $5 \times 5 = 25$

Step3: Calculate area of tall triangles

Area of 2 triangles: $2 \times \frac{1}{2} \times 5 \times 16 = 80$

Step4: Calculate area of short triangles

Area of 2 triangles: $2 \times \frac{1}{2} \times 5 \times 10 = 50$

Step5: Sum all areas

Total surface area = base area + tall triangles area + short triangles area

Answer:

$25 + 80 + 50 = 155$ square inches