Question

A triangle and a parallelogram has same base and same area as shown in the diagram below. Dimensions of triangle are 28cm, 26cm and 30cm with 28cm being the base. What is the height of the parallelogram?

(a) 15cm

(b) 10cm

(c) 12cm

(d) 18cm

I have been asked this question during an interview.

The doubt is from Application of Heron’s Formula in finding Areas of Quadrilaterals topic in division Heron’s Formula of Mathematics – Class 9

Answer 1

Right option is (c) 12cm

To explain: a = 28, b = 26 and c = 30 cm.

s = \(\frac{a+b+c}{2}=\frac{28+26+30}{2} = \frac{84}{2}\) = 42

According to heron’s formula, area of the triangle = \(\sqrt{s*(s-a)*(s-b)*(s-c)}\)

= \(\sqrt{42*(42-28)*(42-26)*(42-30)}\)

= \(\sqrt{42*14*16*12}\)

= 336 cm^2

It is given that area of the triangle and the parallelogram is same.

Now, we know that area of a parallelogram = base * perpendicular (height of a parallelogram)

Therefore, 28 * height  = 336

height = \(\frac{336}{28}\)

height = 12cm.