Question

two diagonal of a parallelogram are 12 cm and 16 cm .if one of its side is 10 cm find the area of parallelogram

Answer 1

let : AB=10 cm.

        AC=12cm

       BD=16cm

Both diagonals intersect at point 'O' and divide other diagonal into 2 equal halfs

So: AO=12/2=6cm

       BO=16/2=8cm

Area of triangle AOB:

semiperimeter=(8+6+10)

                                  12

=12cm

By using heron's formula

area=underoot 12(12-10)(12-8)(12-6)

=underoot12*2*4*6

=underoot 576

=24cm2

Area of parallelogram ABCD= 4* (Area of triangle AOB)

         =4*24

        =96 cm2


Thanks

Answer 2

✬ Area of Parallogram = 96 cm² ✬

Step-by-step explanation:

Given:

• Measure of two diagonals of parallogram are 12 cm and 16 cm respectively.
• Measure of one of the side of parallogram is 10 cm.

To Find:

• What is the area of parallogram?

Solution: Let ABCD be a Parallelogram in which :-

• Diagonal = AC = 12 cm and
• Diagonal = BD = 16 cm

• We know that the diagonals of a parallogram bisect each other •

∴ OA = OC = 1/2 AC

=> OA = OC = 1/2 x 12

=> OA = OC = 6 cm similarly

∴ OD = OB = 1/2 BD

=> OD = OB = 1/2 x 16

=> OD = OB = 8 cm

• In ∆OAB we have to find area by Heron's formula •

★ Semi Perimeter (S) = (a + b + c/2) ★

$\implies{\rm }$ Semi Perimeter = (6 + 8 + 10/2)

$\implies{\rm }$ 24/2 = 12

★ Heron's Formula ∆= √S(s–a) (s–b) (s–c) ★

$\implies{\rm }$ Area of ∆OAB = √12(12–6) (12–8) (12–10) cm²

$\implies{\rm }$ √12 x 6 x 4 x 2 cm²

$\implies{\rm }$ √576 cm²

$\implies{\rm }$ √ 24 x 24 cm²

$\implies{\rm }$ 24 cm²

Hence, area of ∆OAB is 24 cm², similarly area of remaining three triangles will be also 24 cm²

• Since, there are 4 triangles of equal areas are under parallogram ABCD

∴ Area of parallogram ABCD =

$\implies{\rm }$ 4 x Area of each triangle

$\implies{\rm }$ (4 x 24) cm²

$\implies{\rm }$ 96 cm²

So, The area of parallogram will be 96 cm²