Question

Trapezoid diagonals are 20 cm and 15 cm and height/altitude is 12 cm. Find the trapezoid area.​

Answer 1

`150cm^2`

Explanation:

`area =`
`(1)/(2) * 12 * (y + x + y + z)`

`area =`
`6 * (x + 2y + z)`

`(y + z)^2 + 12^2 = 20^2`
`and`
`(x + y)^2 + 12^2 = 15^2`

`(y + z) =`
`√(20^2-12^2)`

−−−−−−−−
`= 16cm`

`(x + y) =`
`√(15^2-12^2)`

−−−−−−−−
`= 9cm`

`area =`
`(1)/(2) * 12 * (√(20^2-12^2) + √(15^2-12^2))`

`area = \\`
`6 * (16+9)`

`area = 150cm^2`

Pythagorean Theorem

We can apply this by breaking down the trapezoid in two triangles.

`base =`
`√((20^2 - 12^2)) + \sqrt{(15^2 - 12^2)`

`base =`
`25`

`area =`
`(1)/(2)bh`

`area =`
`(1)/(2) * 25 * 12`

`area =`
`150cm^2`