Question

Find the area of the shape.​

Answer 1

Answer:

868 cm²

Step-by-step explanation:

The area of the given shape can be expressed as the sum of the area of the trapezium and the area of the semi-circle.

So,

Area = Area of trapezium + Area of Semi-Circle

First, let's find out the area of the trapezium.

The formula to calculate the area of a trapezium is

$\frac{1}2 (a + b) h$

Where,

a and b are the parallel sides of the trapezium.

h is the perpendicular height of the trapezium.

a = 28cm

b = 42cm

h = 16cm

∴ Area = $\frac{1}2(28 + 42)16$

            = 70 × 8

            = 560 cm²

Now, we must find the area of the semi-circle.

We know that the area of a circle = $\pi r^2$

We also know that a semi-circle is a circle which has been divided exactly into half.

Hence, the area of the semi-circle will be

$\frac{\pi r^2}2$

Since the value of pi has not been specified here, we can take $\pi = \frac{22}7$ for easier calculations.

Now, the common knowledge of circles is that the diameter of a circle is twice the radius.

The diameter given here is 28cm.

Hence,

Radius = $\frac{28}2$

            = 14cm

∴ Area of semi-circle = $\frac{\frac{22}7 * 14 * 14}{2}$

                                   = 22 × 14

                                   = 308 cm²

Now, we have to add the area of the trapezium and the semi-circle to obtain the total area of the whole figure.

We get

308 + 560

= 868 cm²