Question

Find the surface area of the square pyramid.

A) 35 ft^2
B) 30 ft^2
C) 45 ft^2
D) 20 ft^2

Answer 1

Area of base

• side²
• 5²
• 25ft²

Area of one triangle side

• 1/2(2)(5)=5ft²

Area of 4 sides

• 5(4)=20ft²

TSA

20+25=45ft²

Answer 2

C) 45 ft²

Explanation:

Formulae

Area of a square = x² (where x is the side length)

Area of a triangle = 1/2 × base × height

The surface area of a square pyramid comprises:

• square base
• 4 congruent triangles

⇒ area of square base = 5² = 25 ft²

⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²

⇒ Total surface area = area of square base + 4 triangular areas

= 25 + 4(5)

= 25 + 20

= 45 ft²