Question

find the area of parallelogram ABCD given in lenght = 5 cm , breadth = 7 cm , diagonal = 8cm.​

Answer 1

Answer:

20√3 cm²

Step-by-step explanation:

Length of a parallelogram AB = 5 cm

Breadth of a parallelogram BC = 7 cm

Diagonal of a parallelogram AC = 8 cm

Area of parallelogram ABCD can be considered as a twice of area of triangle ABC.

Calculating area of triangle ABC:

Perimeter of triangle = 20 cm

Semi perimeter (s) = 20 cm/2 = 10 cm

Using formula

Area of triangle ABC = √[(s)(s-a)(s-b)(s-c)]

Area of triangle ABC = √[(10cm) (10-5)cm (10-7)cm (10-8)cm]

Area of triangle ABC = √[(10cm) (5cm) (3cm) (2cm)]

Area of triangle ABC = 10√3 cm²

Now,

Area of parallelogram ABCD = 2 × Area of triangle ABC

Area of parallelogram ABCD = 2 × ( 10√3 cm² )

Area of parallelogram ABCD = 20√3 cm²

Thus, area of parallelogram ABCD = 20√3 cm² .