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maria [59]
3 years ago
9

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.

Mathematics
1 answer:
Elodia [21]3 years ago
8 0

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

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