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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