Question

There is a regular hexagon mnopqr of side 5cm. Aman and ridhima divided it in two different ways. Find the area of hexagon using both ways?

Answer 1

Answer:

Step-by-step explanation:

There are two ways of finding the area.

1) Dividing the hexagon into 6 equilateral triangles and getting the area of one triangle multiplied by 6.

2) Dividing the hexagon into two trapezium and getting the area of individual trapezium.

First we need the height of the equilateral triangle.

By pythagorean theorem we have :

5^2 - 2.5^2 = 18.75

Square root of 18.75 = 4.330

1) Area of one equilateral triangle :

4.330 × 0.5 × 5 = 10.825

For the six :

6 × 10.825 = 64.95 square centimeters.

2) The area of the trapezium is :

The two parallel sides of the trapezium are 10cm and 5 cm.

The height is 4.30cm

Area :

(10 + 5) /2 × 4.30 = 32.25

We have two trapezium.

2 × 32.28 = 64.5 square centimeter.