Question

Find the area of the shape shown below.

Answer 1

❏ Solution

Find:-

• Area of shape ABCE

❏ Explanation

For this,

First calculate , area of rectangle ABCD

★ Area of rectangle = ( Length × Width )

Here,

• Length = 12
• width = 6

➥ Area of rectangle ABCD = 12 × 6

➥ Area of rectangle ABCD = 72 unit²

Second calculate , area of right ∆ CDE

★ Area of right ∆ = 1/2 × ( Base) × (Height )

Here,

• Base = 5
• Height = 12

➥ Area of right ∆ CDE = 1/2 × 5 × 12

➥ Area of right ∆ CDE = 5 × 6

➥ Area of right ∆ CDE = 30 unit²

For, area of shape CDE , Subtract area of ∆CDE from area of rectangle ABCD

SO,

★ Area of shape CDE = Area of rectangle ABCD - Area of ∆ CDE

➥ Area of shape CDE = 72 - 30

➥ Area of shape CDE = 42 unit²

Hence:-

• Area of shape CDE = 42 unit²

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Answer 2

Solution (1) :-

Given :-

→ AD = 1cm.

→ AB = 12cm.

→ BC = 6cm.

→ DC = 13cm.

→

Construction :-

• Draw a Line DE parallel to AB ..

→ Area of Rectangle ABED = Length * Breadth = 12 * 1 = 12cm² .

Now, in Right ∆DEC, we have ,

→ EC = BC - BE = 6 - 1 = 5 cm.

→ DE = AB = 12 cm.

So,

→ Area of ∆DEC = (1/2) * Base * Height = (1/2) * 5 * 12 = 30cm².

So,

→ Area Quad.[ABCD] = 12 + 30 = 42cm² (Ans).

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Solution (2) :-

In Quadrilateral ABCD we have ,

→ AD is parallel to BC .

→ AB is height of Quadrilateral as 12cm.

So,

we can conclude That, Quad. ABCD is a Trapezium.

So,

→ Area of Trapezium = (1/2) * ( sum of Parallel Sides) * Height .

→ Area Quad.[ABCD] = (1/2) * (1 + 6) * 12 = 7 * 6 = 42cm². (Ans).

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