Question

Find the areas of the following figures in which all the corners are right-angled and the dimensions are shown
in centimetres.
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Answer 1

Given:-

• A figure with dimensions

To Find:-

• Area of the figure.

Note :-

• Firstly it is necessary to label the figure (refer to the attachment).

Solution:-

Here in the figure we can find 3 rectangles

For rectangle ABCI,

AI || BC

⇒ AI = BC = 6 cm

AB || IC

⇒AB = IC = 12 cm

We know,

• Area of rectangle = Length × Breadth

Hence,

Area = 6 × 12

⇒ Area of rectangle ABIC = 72 cm²

∴ Area of rectangle ABIC is 72 cm²

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Now,

In rectangle IEJD,

DH + HJ = DJ

⇒ DJ = 18 + 20 = 38 cm

⇒ IE || DJ

⇒ IE = DJ = 38 cm

Now,

ID = AD - AI

⇒ ID = 20 - 6

⇒ ID = 14 cm

⇒ ID || EJ

⇒ ID = EJ = 14 cm

Now,

Area = 38 × 14

⇒ Area of rectangle IEJD = 532 cm²

∴ Area of rectangle IEJD is 532 cm²

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Now,

In rectangle HGFJ,

JF || HG

⇒ JF = HG = 6 cm

Also,

HJ || GF

⇒ HJ = GF = 20 cm

Now,

Area = 20 × 6

⇒ Area of rectangle HGFJ = 120 cm²

∴ Area of rectangle HGFJ is 120 cm².

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Now,

Area of the figure is as follows:-

Area of rectangle (ABIC + IEJD + HGFJ)

⇒ Area of the figure = (72 + 532 + 120) cm²

⇒ Area of the figure = 724 cm²

∴ Area of the figure is 724 cm²

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