Question

Find the area of a parallelogram whose adjacent sides are lengths 10 cm and 12 cm and one diagonal is of length 8 cm

Please reply fast

Answer 1

let a parallelogram ABCD
AB=12; BC=10, and diagonal AC=8
area of parallelogram=2(area of triangle ABC)
we can find the area of triangle by using herons formula 
s=(AB+BC+AC)/2=(12+10+8)/2=15
area=under root{15(15-12)(15-10)(15-8)}
       =15√7 cm^2
area of parallelogram=30√7 cm^2

Answer 2

Given,

The two adjacent sides of a parallelogram = 10 cm and 12 cm

One of the diagonals = 8 cm

To find,

The area of the parallelogram.

Solution,

The area of the parallelogram will be 30√7 cm².

We can easily solve this problem by following the given steps.

According to the question,

The two adjacent sides of a parallelogram = 10 cm and 12 cm

One of the diagonals = 8 cm

Let's take ABCD as a parallelogram.

AB (a) = 12 cm

BC (b) = 10 cm

AC (c) = 8 cm

Now, ABC is a triangle of the same area as triangle ADC.

We know that the area of a triangle can be found using Heron's formula:

Semi- perimeter (s) = (a+b+c)/2

's' = (12+10+8)/2

's' = 30/2 cm

's' = 15 cm

Now, using Heron's formula:

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

A = $\sqrt{15(15 - 12)(15 - 10)(15 - 8)}$

A = $\sqrt{15(3)(5)(7)}$

A = $\sqrt{45 \times 35}$

A = $\sqrt{1575}$

A = $15 \sqrt{7}$ cm²

Now,

Area of parallelogram = Area of ∆ ABC + Area of ∆ ADC

Area = (15√7 + 15√7) cm²

Area = 30√7 cm²

Hence, the area of the parallelogram is 30√7 cm².