Question

The measure of two adjacent sides of a parallelogram is 5cm and 4cm. The measure of its one diagonal is 7cm.find its area.

Answer 1

Answer:

20cm²

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Answer 2

The area is 19.56

Explanation:

Given,

Two adjacent sides of parallelogram is 5 cm and 4 cm .

Diagonal is 7 cm

Find,

The area of the parallelogram

Lets take parallelogram as ABCD

The parallelogram ABCD divides into two triangles.

The two triangles are DAB and DCB

Formula for finding the area of parallelogram is

Area of ABCD = 2× Area of triangle ABD

Side of the parallelogram AB = 5 cm

Side of the parallelogram AD= 4 cm

Diagonal DB = 7 cm

We use heron's formula

heron's formula = $\sqrt{s (s-a)(s-b)(s-c)}$

where s = $\frac{a+b+c}{2}$

a = 4 cm

b = 5 cm

c = 7 cm

substitute  the above value in s.

s = $\frac{4+5+7}{2}$ = 8

Therefore,

Area of triangle = $\sqrt{s (s-a)(s-b)(s-c)}$

                          = $\sqrt{8 (8-4)(8-5)(8-7)}$

                          = $\sqrt{96}$

                          = 9.78

Now ,

Multiply the area of triangle twice

Area of parallelogram ABCD = 2× Area of triangle

Area of parallelogram ABCD = 2× 9.78 = 19.56

∴ Area of parallelogram = 19.56