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]
