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 = `sqrt(400)`

= 20 cm

Area of the right angle triangle = `1/2` bh sq.unit

= `1/2 xx 12 xx 16  "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 = `("a" + "b" + "c")/2`

= `(42 + 34 + 20)/2 "cm"`

= `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

= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`

= `sqrt(48 xx 6 xx 14 xx 28)`

= `sqrt(2^4 xx 3 xx 2 xx 3 xx 2 xx 7 xx 2^2 xx 7)`

= `sqrt(2^8 xx 3^2 xx 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