Question

If x = 9 units, y = 3 units, and h = 8 units, find the area of the rhombus shown above using decomposition.

Answer 1

Answer: area 72

Explanation:

Answer 2

`Area = 96`

Explanation:

Given

`x = 9`
`y =3`
`h = 8`

See attachment for rhombus

Required

Determine the area

From the attached rhombus:

We have

(1) Triangle

`Base = x;\ \ Height = h`

The area is:

`Area = 0.5 * Base * Height`

`A_1= 0.5 * x*h`

`A_1 = 0.5 * 9 *8`

`A_1 = 36`

(2) Triangle

`Base = y;\ \ Height = h`

The area is:

`Area = 0.5 * Base * Height`

`A_2 =0.5 * y * h`

`A_2 =0.5 * 3 * 8`

`A_2 =12`

(3) Rectangle

`Area = Length * Width`

`Length =h; Width = x - y`

because all sides are equal, so the remaining side is x - y

So:

`A_3 = h * (x - y)`

`A_3 = 8 * (9 - 3)`

`A_3 = 8 * 6`

`A_3 = 48`

So, the area is:

`Area = A_1 + A_2 + A_3`

`Area = 36 + 12 + 48`

`Area = 96`