Question

a rectangular pyramid is shown below.which diagram is a net for this pyramid?what is the surface area of the rectangular pyramid?square inches

Explanation:

Step1: Identify correct net

The rectangular pyramid has a square base (8 in x 8 in) with two pairs of congruent triangular faces: two triangles with slant height 12 in, two with slant height 13 in. The left net matches this (base 8x8, two triangles with height 12, two with height 13).

Step2: Calculate base area

Find area of the square base.
$\text{Base Area} = 8 \times 8 = 64$

Step3: Calculate area of 12-in slant triangles

Find area of two triangles with slant height 12.
$\text{Area of 2 triangles} = 2 \times \frac{1}{2} \times 8 \times 12 = 96$

Step4: Calculate area of 13-in slant triangles

Find area of two triangles with slant height 13.
$\text{Area of 2 triangles} = 2 \times \frac{1}{2} \times 8 \times 13 = 104$

Step5: Sum all areas for surface area

Add base and triangular face areas.
$\text{Surface Area} = 64 + 96 + 104$

Answer:

1. Correct net: The left diagram (with square base 8 in x 8 in, two triangles with height 12 in, two triangles with height 13 in)
2. Surface Area: 264 square inches