Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9

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 - Mathematics

Sum

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

Solution

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

Is there an error in this question or solution?
Chapter 7: Mensuration - Exercise 7.1 [Page 253]