Question

Fede area of a parallelogram ABCD in
which AB = 25 cm, BC = 26 cm and diagonal
AC = 30 cm​

Answer 1

Answer:

Find the area of a parallelogram ABCD in which AB = 28cm, BC = 26cm and diagonal AC = 30 cm. Answer. Let the sides ...

Missing: Fede ‎| Must include: Fede

Answer 2

Given :

• Length of AB = 25 cm
• Length of BC = 26 cm
• Length of AC = 30 cm

To Find :

The Area of the Parallelogram !!

Solution :

Before moving further , let's have some information about a parallelogram.

⠀⠀⠀⠀⠀⠀⠀⠀⠀Definition :

A quadrilateral is Parallelogram when the it's diagonals are equal and parallel.

⠀⠀⠀⠀⠀Laws of a Parallelogram :(Here needed)

1) Opposite sides of a parallelogram are equal.

2) A diagonal of Parallelogram divides it into two equal triangles by SAS property.

Now , from the first property of the Parallelogram , we get that AB = DC and BC = AD.

Hence, we get the Sides as :

• AB = DC = 25 cm
• BC = AD = 26 cm

From the second property , we get that ∆ ABC = ∆ ADC.

Hence , the sum of the areas of both the triangles will give the area of the Parallelogram.

Thus , equation formed is :

$\underline{\bf{Area\:of\:\triangle\:(ABC + \triangle\:ADC) = Area\:of\:ABCD}}$

⠀⠀⠀⠀⠀⠀⠀To find the area of triangles :

Since all the sides are unequal , the given triangle is a Scalene triangle.

So , the area of an Scalene triangle can be found by using the heron's formula !

⠀⠀⠀⠀Heron's formula –

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

Where :

• a , b and c are the sides of the triangle.

• s = Semi-perimeter

$\bf{s = \bigg(\dfrac{a + b + c}{2}\bigg)}$

So first let find the semi-perimeter of the triangle (same in both the cases)

So , using the formula and substituting the values in it, we get :

$:\implies \bf{s = \bigg(\dfrac{25 + 26 + 30}{2}\bigg)}$

$:\implies \bf{s = \dfrac{81}{2}}$

$:\implies \bf{s = 40.5\:cm}$

So , the semi-perimeter of the triangle is 40.5 cm.

Now , using the formula for area of a Scalene triangle and substituting the values in it, we get :

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

Since, both the triangles are equal , we multiply the area of the triangle by 2.

$:\implies \bf{A = 2 \times \sqrt{40.5(40.5 - 25)(40.5 - 26)(40.5 - 30)}}$

$:\implies \bf{A =\ 2 \times sqrt{40.5 \times 15.5 \times 14.5 \times 10.5)}}$

$:\implies \bf{A = 2 \times \sqrt{95574.93}}$

$:\implies \bf{A = 2 \times 309.15}$

$:\implies \bf{A = 618.30}$

$\therefore \bf{Area = 618.30\:cm^{2}}$

Hence, the area of both the equal triangles is 618

30 cm².

Since , we know that the area of the two triangles will give the area of the Parallelogram.

Thus, the area of the Parallelogram is 618.30 cm².