Question

find the area of a parallelogram ABCD in which AB=28cm,BC=26cm and diagonal AC=30cm

Answer 1

$\text{Given...}\\AB = 28 \ cm\\BC = 26 \ cm\\\text{It seems to be a rectangle..}\\\\\text{Hence, Area = }l\times b=28\times 26 \\\boxed{\boxed{Area = 728\ cm^2}}$

Answer 2

Step-by-step explanation:

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Given,

AB = 28cm

BC = 26cm

AC = 30cm.

Find,

The area of a parallelogram ABCD.

SO,

Let the sides of the triangle ABC be:

a = 26cm

b = 30cm

c = 28cm

Let us find out the value of s.

We know that,

s = 1/2 (a + b + c)

=> s = 1/2(26 + 30 + 28)

=> s = 84/2

=> s = 42cm.

We know that,

Area of triangle ABC = √s(s - a)(s - b)(s - c)

=> √42(42 - 26)(42 - 30)(42 - 28)

=> √42 × 16 × 12 × 14

=> √14 × 3 × 16 × 4 × 3 × 14

=> √14 × 14 × 3 × 3 × 16 × 4

=> 14 × 3 × 4 × 2

=> 336cm².

We know that,

In a parallelogram, the diagonal divides the parallelogram in two equal area.

Therefore,

Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD

=> Area of triangle ABC × 2

=> 336 × 2

=> 672cm².

Hence,

The area of parallelogram is 672cm².