Question

What is the area of this composite shape?

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in²

Answer 1

your answer is 62. the area of the triangle is 6 the area of the rectangle is 56.

Answer 2

Labeled the diagram as shown below.,

In rectangle ABCD:

Area of the rectangle(A) is given by:

`\text{A} = \text{Lenght} \cdot \text{Width}`

From the diagram:

AB = DC = 8 in. and AD = BC = 7 in.

⇒Length = 7 in. and width = 8 in.

then;

`\text{Area of rectangle ABCD} = 7 \cdot 8 = 56 in^2`

Next, find the area of triangle OAE:

`\text{Area of triangle} = (1)/(2) \cdot \text{Base} \cdot \text{Height}`

In triangle OAE

Base = AE = 3 in.

Height = OA = 4 in.

then;

`\text{Area of triangle OAE} = (1)/(2) \cdot 3 \cdot 4 = 3 \cdot 2 = 6 in^2`

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