Question

12. A parallelogram has two sides 50 m and 30 m and a diagonal 70 m long. Find the
area of the parallelogram.​

Answer 1

Answer:

area of the parallelogram =base×height

Step-by-step explanation:

50 is the base

Answer 2

To Find:-

• The are of parallelogram

Solution:-

Let ABCD be parallelogram filled field with sides AB = CD = 50m , BC = DA = 30 and Diagonal BD = 70 m

step-by-step explanation:

Area of the parallelogram = 2 ( Area of ∆ABD )

So, In triangle ABD,

Semi-perimeter of ∆ABD,

$s = \dfrac{a + b + c}{2}$

$s = \dfrac{AB + BD + DA}{2}$

$= \dfrac{50 + 70 + 30}{2}$

$= \dfrac{150}{2}$

$= 75m$

Now,

The area of ∆ABD by ( heron's formula )

$\sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{75(75 - 50)(75 - 70)(75 - 30)}$

$\sqrt{75 \times 25 \times 5 \times 45}$

$372 \sqrt{3}$

So,

Area of the Parallelogram ABCD is

= 2 × 372√3

= 744√3 m²

Required Answer:-

744√3 m²