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# The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is

(a) 72 cm²

(b) 36 cm²

(c) 24 cm²

(d) 18 cm²

**Solution:**

Since AB = CD and DC = AD we can infer that

△ABC = △ADC (Congruent Triangles satisfying the condition AAA)

Hence the area of the triangles will be equal.

The altitude of △ABC = 3cm

The base of △ABC = 12 cm

Area of the △ABC = (½)(Base(Height) = (½)(12)(3) = 18 cm²

Area of quadrilateral ABCD = Area of △ABC + Area of △ADC

Since △ABC = △ADC

Area of quadrilateral ABCD = 18 + 18 = 36 cm²

The answer is choice (b)

**✦ Try This: **The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is (a) 56 cm², (b) 36 cm², (c) 48 cm², (d) 54cm²

Since AB = CD and DC = AD we can infer that

△ABC = △ADC (Congruent Triangles satisfying the condition AAA)

Hence the area of the triangle will be equal.

The altitude of △ABC = 4cm

The base of △ABC = 14 cm

Area of the △ABC = (1/2)(Base(Height) = (1/2)(14)(4) = 28 cm²

Area of quadrilateral ABCD = Area of △ABC + Area of △ADC

Since △ABC = △ADC

Area of quadrilateral ABCD = 28 + 28 = 56 cm²

The answer is choice (a)

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 11

**NCERT Exemplar Class 8 Maths Chapter 11 Problem 16**

## The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is (a) 72 cm² (b)36 cm² (c) 24 cm² (d) 18 cm²

**Summary:**

The figure ABCD is a quadrilateral in which AB = CD and BC = AD. Its area is 36 cm²

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