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

Answer:

46 cm²

Step-by-step 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= $width\times length$

⇒$36= 9cm\times l$

dividing both side by 9 cm.

∴ $l= \frac{36}{9} = 4\ cm$

Hence, NC= 4 cm

Next, finding the area of triangle ΔNBC

Area of triangle= $\frac{1}{2} \times (base\times height)$

⇒ Δ NBC= $\frac{1}{2} \times 5\times 4$

∴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