Question

The area of the parallelogram abcd is 90 cm². Find ar (|| gm ABEF) (ii) ar ( triangle ABD) (iii) ar ( triangle BEF)


PLZ REFER THE PICTURE ABOVE​

Answer 1

Answer:

The answer will be:

(i) ar (|| gm ABEF) = 90cm^2

(ii) ar ( triangle ABD) = 45 cm^2

(iii) ar ( triangle BEF) = 45 cm^2

Step-by-step explanation:

We have given;

ar (parallelogram ABCD) = 90cm^2;

Now we know that area of two parallelogram equals;

1/2 * base * hieght;

Hence, area of ABCD = area of ABEF (since both have same base and equal hieght)

Therefore, area of parallelogram ABEF = 90 cm^2. (i)

From the given figure, we can write that,

Area of parallelogram ABCD = area of triangle ABD + area of triangle CDB. (ii)

In triangles ABD and CDB;

AB = CD. {equal sides

AD = BC of a parallelogram}

BD = BD (common)

Hence, triangle ABD is congruent to triangle CDB by SSS criteria of congruence.

Thus, ar(ABD) = ar(CDB) (iii)

Using equation (ii) and (iii), we can deduce;

Area of parallelogram ABCD = area of triangle ABD + area of triangle ABD.

90 cm^2 = 2 {area of trianle ABD}

Area of triangle ABD= 45 cm^2.

In similar way, triangle BEF and FAB will be congruent.

Thus, area of triangle BEF = area of triangle FAB

Hence, 2{area of BEF} = area of parallelogram ABEF;

2{area of BEF} = 90cm^2; (from equation (i))

area of triangle BEF = 45 cm^2.

That's all.