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प्रश्न
The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of the diagonal is 42 m. Find the area of parallelogram
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उत्तर
Since ABCD is a parallelogram opposite sides are equal.
In the ΔABC
a = 20 m, b = 42 m and c = 34 m
s = `("a" + "b" + "c")/2`
= `(20 + 42 + 34)/2 "cm"`
= `96/2`
= 48 m
s – a = 48 – 20 = 28 m
s – b = 48 – 42 = 6 m
s – c = 48 – 34 = 14 m
Area of the ΔABC
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`
= `sqrt(48 xx 28 xx 6 xx 14)`
= `sqrt(2^4 xx 3 xx 2^2 xx 7 xx 2 xx 3 xx 2 xx 7)`
= `sqrt(2^8 xx 3^2 xx 7^2)`
= 24 × 3 × 7 sq.m
= 16 × 3 × 7 sq.m
= 336 sq.m
Since ABCD is a parallelogram
Area of ΔABC and Area of ΔACD are equal
Area of the parallelogram ABCD = (336 + 336) sq.m
= 672 sq.m
∴ Area of the parallelogram = 672 sq.m
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