Question

ΔABC and ΔADE are two equilateral triangles is which AB = 12 cm and AD = 6 cm. Find the area of the shaded region. `("Use" sqrt(3) = 1.73)`

Answer 1

Given:

ΔABC and ΔADE are equilateral.

AB = 12 cm   ...(So side of large triangle = 12)

AD = 6 cm   ...(So side of small triangle = 6)

Use `sqrt(3) = 1.73`   ...`("Area formula for an equilateral triangle": sqrt(3)/4 xx a^2)`

Step-wise calculation:

1. Area (ΔABC) = `sqrt(3)/4 xx AB^2` 

= `1.73/4 xx 12^2`

= `1.73/4 xx 144` 

= 1.73 × 36

= 62.28 cm²

2. Area (ΔADE) = `sqrt(3)/4 xx AD^2` 

= `1.73/4 xx 6^2`

= `1.73/4 xx 36` 

= 1.73 × 9

= 15.57 cm²

3. Shaded region = Area (ΔABC) – Area (ΔADE)

= 62.28 – 15.57

= 46.71 cm²

Area of the shaded region = 46.71 cm².