Question

Alison is going camping and needs to buy a canvas tarp to cover the top of her tent, which is in the shape of a square pyramid. A diagram of the tent is shown. How large of a canvas tarp does she need to buy?

A) 80 ft2
B) 105 ft2
C) 160 ft2
D) 185 ft2

Answer 1

80 ft2

Explanation:

I put 105 ft2 but that was wrong.

Answer 2

Alison needs to buy a canvas tarp sized B) 105 ft².

Explanation:

Step 1; The square pyramid has a square base with side length 5 feet. There are 4 triangles with base lengths of 5 feet and heights of 8 feet. To calculate the area of the entire canvas tarp we add the areas of the square and the area of the 4 triangles.

Step 2; The area of a square is the square of the side length. The side length is 5 feet.

Area of the square = side length × side length = 5 × 5 = 25 ft².

The area of any triangle is half the product of the base and height.

Area of 1 triangle =
`(1)/(2)` × base × height = 20 ft².

Area of 4 triangles = 4 × Area of 1 triangle = 4 × 20 = 80 ft².

Area of entire shape = Area of square + Area of triangles = 25 + 80 = 105 ft².

So Alison needs 105 ft² of canvas tarp.