Question

1. rectangular pyramid

lateral surface area: ____ total surface area: ____
(there is a diagram of a rectangular pyramid net with relevant length labels: 8 cm, 9.5 cm, 6 cm, 12 cm)

Explanation:

Step1: Calculate area of 12cm triangles

The two triangles with base 12 cm and height 8 cm:
Area of one: $\frac{1}{2} \times 12 \times 8 = 48$ cm²
Total for two: $2 \times 48 = 96$ cm²

Step2: Calculate area of 6cm triangles

The two triangles with base 6 cm and height 9.5 cm:
Area of one: $\frac{1}{2} \times 6 \times 9.5 = 28.5$ cm²
Total for two: $2 \times 28.5 = 57$ cm²

Step3: Find lateral surface area

Sum the areas of all 4 triangular faces:
$96 + 57 = 153$ cm²

Step4: Calculate base rectangle area

Area of the rectangular base: $12 \times 6 = 72$ cm²

Step5: Find total surface area

Add lateral area and base area:
$153 + 72 = 225$ cm²

Answer:

lateral surface area: $153$ cm²
total surface area: $225$ cm²