Ex 11.4, 11 Find the area of the quadrilateral ABCD. Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM ⊥ AC, DN ⊥ AC
Area of quadrilateral ABCD = Area of ∆ABC + Area of ∆ADC
Area of ∆ABC
Base = b = AC
= 22 cm
Height = BM
= 3 cm
Area of ∆ABC = 1/2 × b × h
= 1/2 × AC × BM
= 1/2 × 22 × 3
= 1/1 × 11 × 3
= 33 cm2
Area of ∆ABC
Base = b = AC
= 22 cm
Height = BM
= 3 cm
Area of ∆ABC = 1/2 × b × h
Area of ∆ADC
Base = b = AC
= 22 cm
Height = ND
= 3 cm
Area of ∆ABC = 1/2 × b × h
= 1/2 × AC × BM
= 1/2 × 22 × 3
= 1/1 × 11 × 3
= 33 cm2
= 1/2 × AC × ND
= 1/2 × 22 × 3
= 1/1 × 11 × 3
= 33 cm2
Therefore,
Area of quadrilateral ABCD
= Area of ∆ABC + Area of ∆ADC
= 33 + 33
= 66 cm2
∴ Area of quadrilateral is 66 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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