Question

The lengths of two adjacent sides of a parallelogram are 10 cm and 15 cm and the distance between the longer sides is 12 cm. Its area is

Answer 1

Answer:

Q. Two adjacent sides of a parallelogram are 10 cm and 12 cm. If one diagonal of it is 16 cm long; find area of the parallelogram. Also, find distance between its shorter sides.

Given, AB=12 cm, BC=10 cm

BD is the diagonal of parallelogram ABCD.

Also BD=16 cm

We know, △ABD≅△DCB [S−S−S Congruence]

Also, area of parallelogram ABCD = Area of △ABD + Area of △DCB

= 2 × Area of △ABD

= 2

s(s−12)(s−10)(s−16)

s=

2

12+10+16

= 19

Therefore, area of parallelogram ABCD= 2

19(19−12)(19−10)(19−16)

= 2

3591

= 2(59.92)

= 119.8 cm

2

Also, h is the distance of the two shorter sides.

We know, area of parallelogram = base×height

= BC×h

Therefore, h=

BC

Area of parallelogram ABCD

⇒h=

10

119.8

⇒h=11.98 cm

solution

Step-by-step explanation:

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