Answer:
Labeled the diagram as shown below.,
In rectangle ABCD:
Area of the rectangle(A) is given by:
[tex]\text{A} = \text{Lenght} \cdot \text{Width}[/tex]
From the diagram:
AB = DC = 8 in. and AD = BC = 7 in.
⇒Length = 7 in. and width = 8 in.
then;
[tex]\text{Area of rectangle ABCD} = 7 \cdot 8 = 56 in^2[/tex]
Next, find the area of triangle OAE:
[tex]\text{Area of triangle} = \frac{1}{2} \cdot \text{Base} \cdot \text{Height}[/tex]
In triangle OAE
Base = AE = 3 in.
Height = OA = 4 in.
then;
[tex]\text{Area of triangle OAE} = \frac{1}{2} \cdot 3 \cdot 4 = 3 \cdot 2 = 6 in^2[/tex]
Area of this composite figure = area of rectangle ABCD+ area of triangle OAE
⇒Area of this composite figure = 56 +6 = 62 square inches.
therefore, area of this composite shape is, 62 in²
