Question

Find the area of a parallelogram ABCD in which AB=14 cm, BC= 10 cm, and AC= 16 cm

Answer 1

Answer:

In ΔABC

Take a = 10cm, b = 16cm and c = 14cm

So we get

s=

2

a+b+c

s=

2

10+16+14

By division

s=20cm

We know that

Area=

s(s−a)(s−b)(s−c)

By substituting the values

Area=

20(20−10)(20−16)(20−14)

So we get

Area=

10×2×10×4×3×2

It can be written as

Area=

10×10×4×2×2×3

On further calculation

Area=10×2×2×

3

So we get

Area=14×3×4×2

By multiplication

Area=40

3

We know that the diagonal divides the parallelogram into two equal area

So we get

Area of parallelogram ABCD=Area of Δ ABC+Area of ΔACD

It can be written as

Area of parallelogram ABCD=2(Area of ΔABC)

By substituting the values

Area of parallelogram ABCD=2(40

3

)

So we get

Area of parallelogram ABCD=80

3

By substituting

3

Area of parallelogram ABCD = 80(1.73)

So we get

Area of parallelogram ABCD =138.4cm

2

Therefore, the area of parallelogram ABCD is 138.4cm