Question

Find the area of the Composite Shape.

PLEASE HELP! ​

Answer 1

`\large\boxed{41.14 inches^2(2 d.p)}`

`\large\boxed{41.1inches^2 (1 d.p)}`

Explanation:

Important Information:

Area of a circle=
`\pi r^2`

Area of a triangle=
`(base*height)/(2)`

Diameter of a cirlce=
`2*radius`

Method:

The first step is to divide the shape into smaller shapes. In this case, we have a right -angled triangle and a semi-circle.

The next step is to work out the area of the triangle. Since we know the radius of the semi-circle is 3 inches, to work out the diameter we would simply multiply the radius of 3 by 2, this gives us 6 inches. This is because the radius is half of the diameter.

Now that we know the diameter of the semi-cirlce, we can begin to work out the area of the triangle. We can do this by first multiplying the base of 6 inches by the height of 9 inches, this gives us 54 inches squared. This however gives us the area of 2 of those triangles. To work out the area of that triangle, we would need to divide the value of 54 by 2, this gives us 27 inches squared.

The next step is to work out the area of the semi-circle. We can do this by multiplying pi by the radius of 3, squared, this gives us 28.27 inches squared (2 d.p). However, this is for a full circle and we need to work out the area of the semi-circle. We can do this by dividing the area of the circle, which is 28.27, by 2, this gives us 14.14 inches squared (2 d.p). This is because a semi-cirlce is half of a circle.

The final step is to add the Areas of the two shapes together. You can do this by adding the area of the triangle, which is 27 inches squared, to the area of the semi circle, which is 14.14 inches squared (2 d.p), this gives us 41.14 inches squared (2 d.p).

Step by Step:

1) Multiply 3 by 2.

`3*2=6`

2) Multiply 6 by 9.

`6*9=54 inches^2`

3) Divide 54 by 2.

`54/2=27inches^2`

4) Multiply pi by 3 squared.

`\pi*3^2=28.27 inches^2 (2 d.p)`

5) Divide 28.27 by 2.

`28.27/2=14.14inches^2 (2 d.p)`

6) Add 27 to 14.14.

`27+14.14=41.14inches^2 (2 d.p)`