Question

the nets of two square pyramids. determine which one has a greater total surface area.

Explanation:

for Pyramid A:

Step1: Calculate base area

The base is a square with side \( 9 \) ft. Area of base: \( 9\times9 = 81 \) square feet.

Step2: Calculate lateral face area

Each lateral face is a triangle with base \( 9 \) ft and height \( 8 \) ft. Area of one triangle: \( \frac{1}{2}\times9\times8 = 36 \) square feet. There are 4 lateral faces, so total lateral area: \( 4\times36 = 144 \) square feet.

Step3: Total surface area of A

Total surface area = base area + lateral area = \( 81 + 144 = 225 \) square feet.

for Pyramid B:

Step1: Calculate base area

The base is a square with side \( 12 \) ft. Area of base: \( 12\times12 = 144 \) square feet.

Step2: Calculate lateral face area

Each lateral face is a triangle with base \( 12 \) ft and height \( 7 \) ft. Area of one triangle: \( \frac{1}{2}\times12\times7 = 42 \) square feet. There are 4 lateral faces, so total lateral area: \( 4\times42 = 168 \) square feet.

Step3: Total surface area of B

Total surface area = base area + lateral area = \( 144 + 168 = 312 \) square feet.

Step4: Compare surface areas

Since \( 225<312 \), Pyramid B has a greater total surface area.

Answer:

Pyramid B (with side 12 ft and triangular height 7 ft) has a greater total surface area.