Mathematics
Find the area of the quadrilateral ABCD shown in figure (ii) given below. All measurements are in centimeters.
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Mensuration
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Answer
In right angle △ABD,
⇒ BD2 = AB2 + AD2
⇒ BD2 = 62 + 82
⇒ BD2 = 36 + 64
⇒ BD2 = 100
⇒ BD = = 10 cm.
In right angle △BDC,
⇒ BC2 = BD2 + DC2
⇒ 262 = 102 + DC2
⇒ DC2 = 676 - 100
⇒ DC2 = 576
⇒ DC = = 24 cm.
Area of △ABD = × base × height
= × AD × AB
= × 8 × 6
= 24 cm2.
Area of △BDC = × base × height
= × DC × BD
= × 24 × 10
= 120 cm2.
Area of quadrilateral ABCD = Area of △ABD + Area of △BDC
= 24 + 120 = 144 cm2.
Hence, area of quadrilateral ABCD = 144 cm2.
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