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प्रश्न
Find the area and the perimeter of quadrilateral ABCD, given below; if AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.
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उत्तर
Given, AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°
BC = `sqrt("DC"^2 - "BD"^2)`
= `sqrt( 13^2 - 12^2 )`
= 5 cm
Hence, perimeter = 8 + 10 + 13 + 5 = 36 cm
Area of ΔABD, `sqrt("s"("s"-"a")("s"-"b")("s"-"c"))`
Here, s = `("a"+"b"+"c")/2`
= `(10+12+8)/2`
= `30/2`
= 15 cm
ΔABD = `sqrt( 15( 15 - 8 )( 15 - 10 )( 15 - 12 ))`
= `sqrt( 15 xx 7 xx 5 xx 3 )`
= `15sqrt7`
= 39.7
Area of ΔBDC,
ΔBDC = `1/2` × 12 × 5
= 30
Now,
Area of ABCD = area of ΔABD + area of ΔBDC
= 39.7 + 30
= 69.7 sq.cm
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