Question

Find the area of a regular hexagon abcdef in which each side measures 13 cm and whose height is 23cm

Answer 1

897 Square centimeters.

Step-by-step explanation:

A regular hexagon has six sides.

To get its area we divide it into six equilateral triangle.

The triangles are of :

Height = 23 cm

Base = 13 cm

Area of a triangle = 1/2 × base × height

We have :

0.5 × 13 × 23 = 149.5 cm squared.

This is the area of one triangle.

The area of the six triangles is :

149.5 × 6 = 897

Area of the hexagon = 897 square centimeters.

Answer 2

Diagram:-

Given:-

• A hexagon ABCDEF in each side measure 13cm and height is 23cm.

To find:-

• Fine the area of a regular hexagon.

Solutions:-

• Let AL = DM = x cm
• LM = BC = 13cm

⟹ x + 13 + x = 23

⟹ 2x + 13 = 23

⟹ 2x = 23 - 13

⟹ 2x = 10

⟹ x = 10/2

⟹ x = 5cm

• AL = 5cm

From the right ∆AFL, we have.

⟹ FL² = AF² - AL²

⟹ FL² = (13)² - (5)²

⟹ FL² = 169 - 25

⟹ FL² = 144

⟹ FL = √144

⟹ FL = 12cm

• FL = BL = 12cm

Area of the regular hexagon = (Area of the trapezium ADEF) + (Area of the trapezium ABCD)

= 2(Area of the trapezium ADEF)

= 2(1/2 × (AD + EF) × FL)

= 2(1/2 × (23 + 13) × 12)

= 2(1/2 × 36 × 12)

= 2 × 18 × 12

= 432cm²

Hence, the area of the regular hexagon is 432cm².