Question

The shape ABCD is made from a rectangle ANCD and the right-angled triangle NBC. ANB is a straight line. AN=9cm, NB=5cm. The area of rectangle ANCD is 36cm squared. Work out the area of shale ABCD.

Answer 1

46 cm²

Explanation:

Given: ANB is a straight line

AN= 9 cm

NB= 5 cm

Are of rectangle( ANCD)= 36 cm²

Now finding the length of rectangle ANCD.

Lets assume the length of rectangle be "l"

Area of rectangle=
`width* length`

⇒
`36= 9cm* l`

dividing both side by 9 cm.

∴
`l= (36)/(9) = 4\ cm`

Hence, NC= 4 cm

Next, finding the area of triangle ΔNBC

Area of triangle=
`(1)/(2) * (base* height)`

⇒ Δ NBC=
`(1)/(2) * 5* 4`

∴Δ NBC= 10 cm²

We know, the area of ANCD= 36 cm²

∴ Area of ABCD= Area of rectangle+area of triangle

⇒Area of ABCD= 36+10

∴ Area of ABCD= 46 cm²