Question

Find the area of the unshaded region

Answer 1

Since ABD is a right angle triangle

AB² = AD² + BD²

= 12² + 16²

= 144 + 256

= 400

AB = ${\displaystyle \sqrt{400}}$

= 20 cm

Area of the right angle triangle = ${\displaystyle \frac{1}{2}}$ bh sq.unit

= ${\displaystyle \frac{1}{2}\times 12\times 16 {\text{cm}}^2}$

= 6 × 16 cm²

= 96 cm²

To find the Area of the triangle ABC

Here a = 42 cm, b = 34 cm, c = 20 cm

s = ${\displaystyle \frac{\text{a}+\text{b}+\text{c}}{2}}$

= ${\displaystyle \frac{42+34+20}{2}\text{cm}}$

= ${\displaystyle \frac{96}{2}}$

= 48 cm

s – a = 48 – 42 = 6 cm

s – b = 48 – 34 = 14 m

s – c = 48 – 20 = 28 m

Area of triangle

= ${\displaystyle \sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}}$

= ${\displaystyle \sqrt{48\times 6\times 14\times 28}}$

= ${\displaystyle \sqrt{2^4\times 3\times 2\times 3\times 2\times 7\times 2^2\times 7}}$

= ${\displaystyle \sqrt{2^8\times 3^2\times 7^2}}$

= 16 × 3 × 7 cm²

= 336 cm²

Area of the unshaded region = Area of the ΔABC – Area of the ΔABD

= (336 – 96) cm²

= 240 cm²