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

Sagot :

MrRoyal

Answer:

[tex]Area = 96[/tex]

Step-by-step explanation:

Given

[tex]x = 9[/tex]   [tex]y =3[/tex]    [tex]h = 8[/tex]

See attachment for rhombus

Required

Determine the area

From the attached rhombus:

We have

(1) Triangle

[tex]Base = x;\ \ Height = h[/tex]

The area is:

[tex]Area = 0.5 * Base * Height[/tex]

[tex]A_1= 0.5 * x*h[/tex]

[tex]A_1 = 0.5 * 9 *8[/tex]

[tex]A_1 = 36[/tex]

(2) Triangle

[tex]Base = y;\ \ Height = h[/tex]

The area is:

[tex]Area = 0.5 * Base * Height[/tex]

[tex]A_2 =0.5 * y * h[/tex]

[tex]A_2 =0.5 * 3 * 8[/tex]

[tex]A_2 =12[/tex]

(3) Rectangle

[tex]Area = Length * Width[/tex]

[tex]Length =h; Width = x - y[/tex]

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

So:

[tex]A_3 = h * (x - y)[/tex]

[tex]A_3 = 8 * (9 - 3)[/tex]

[tex]A_3 = 8 * 6[/tex]

[tex]A_3 = 48[/tex]

So, the area is:

[tex]Area = A_1 + A_2 + A_3[/tex]

[tex]Area = 36 + 12 + 48[/tex]

[tex]Area = 96[/tex]

View image MrRoyal
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