Question

What is the area of this composite shape?

Answer 1

The above composite shape can be divided into :

● A Rectangle with Length 7 in. and Width 6 in.

● A Right angled Triangle with base 3 in. and height 6 in.

Let us first find the Area of Rectangle :

We know that - Area of a Rectangle is given by : Length × Width

`:\implies` Area of Rectangle = (7 × 6) in²

`:\implies` Area of Rectangle = 42 in²

Now, Let us find the Area of Right angled Triangle :

`\mathsf{We\;know\;that - Area\;of\;a\;Triangle\;is\;given\;by : (1)/(2) * base * height}`

`\implies \mathsf{Area\;of\;Right\;angled\;Triangle = (1)/(2) * 3 * 6\;(in^2)}`

`:\implies` Area of Right angled Triangle = (3 × 3) in²

`:\implies` Area of Right angled Triangle = 9 in²

Area of the Composite shape :

● Area of Rectangle + Area of Right angled Triangle

`:\implies` Area of the Composite shape = (42 + 9) in²

`:\implies` Area of the Composite shape = 51 in²

Answer 2

51 in² is the area of the shape.

Explanation:

Note that there is a triangle, as well as a Parallelogram.

First, solve for the measurement for the Parallelogram. The Parallelogram has sides that measure 6 in. & 7 in. respectively.

Note the measurement of the left length, which is 13. The right length is 7. To solve for the length of the triangle, subtract the two:

13 - 7 = 6

The triangle length is 6.

To solve for the triangle width, subtract the part from the total:

6 - 3 = 3

The triangle width is 3.

Note that the area of the triangle is found using the formula: Area = 1/2base x height (or length x width). Plug in the corresponding numbers to the corresponding variable.

A = 1/2(3)(6)

A = (3)(3)

A = 9

The triangle's area is 9 in².

Solve for the area of the parallelogram:

6 x 7 = 42

The parallelogram's area = 42 in².

Add the two measurements together:

42 + 9 = 51

51 in² is the area of the shape.

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