Question

a parallelogram has 2 adjacent sides of 13 cm and 14 cm and a diagonal of 15 cm, find the area of the parallelogram?

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• A parallelogram has two adjacent sides of $\rm{ \pink{13 \: cm}}$ and $\rm{ \pink{14 \: cm}}$ .

• Diagonal is $\rm{ \pink{15 \: cm}}$ .

To Find :

• Area of the parallelogram.

Calculation :

As we know that,

• Area of parallelogram = 2 × Area of triangle covered by two adjacent sides along with the diagonal.

So, first let's calculate the semiperimeter

Formula to be used :

We'll use heron's formula (for triangle)

• S = $\tt \dfrac{a + b + c}{2}$

Where,

• a = 13 cm
• b = 14 cm
• c = 15 cm

$\dag$ Putting the values,

$\longmapsto \: \sf \dfrac{a + b + c}{2}$

$\longmapsto \sf \dfrac{13 + 14 + 15 \: cm}{2}$

$\longmapsto \sf \cancel \dfrac{42}{2}$

$\longmapsto \bf \: 21 \: cm$

Therefore, semiperimeter is 21 cm.

Now, let us calculate the area by using heron's formulae :-

• $\tt \: \sqrt{s(s - a)(s - b)(s - c) \: sq. \: unit}$

$\dag$ Putting the values,

$\longmapsto \sf \sqrt{21(21 - 13)(21 - 14)(21 - 15)}$

$\longmapsto \sf \sqrt{3 \times 7 \times 4 \times 2 \times 7 \times 2 \times 3}$

$\longmapsto \sf 2 \times 2 \times 3 \times 7$

$\longmapsto \bf 84 \: cm^2$

~ Performing multiplication :

$\longmapsto \sf \: 2 \: \times \: 84 \: cm^2$

$\longmapsto \bf \: 168 \: cm^2$

Therefore, area of parallelogram is $\rm \: { \purple{168 \: cm^2}}$ .