Question

The roof on Crystal’s house is formed by two congruent trapezoids and two congruent isosceles triangles. She wants to put new wood shingles on her roof. Each shingle will cover 0.25 square foot of area. (The shingles are 1 foot by 1 foot, but they overlap by 0.75 square foot.) How many shingles should Crystal buy?

Answer 1

the total number of shingles is 3060

Explanation:

Please have a look at the attached photo.

We need to find the total are of the roof.

The are of the trapezoid is:

• A = 1/2 (base 1 + base 2) height

= 1/2 (20+30)*15

= 375
`ft^(2)`

The are of the triangle:

• A = 1/2*base*height

= 1/2(1.5*10)

= 7.5
`ft^(2)`

=> We need to find the total are of the roof is:

The are of the 2 trapezoids + The are of the 2 triangles

= 375
`ft^(2)`*2 + 7.5
`ft^(2)` *2

= 765
`ft^(2)`

Given in the question that, the shingles are 1 foot by 1 foot, but they overlap by 0.75 square foot so the usable area of the shingle is only 0.25
`ft^(2)`

So the total number of shingles is:

765
`ft^(2)` / 0.25
`ft^(2)`

= 3060