Question

Find the area of a parallelogram given in figure. Also find the length of the altitude from vertex A on the side DC.

Answer 1

Let the sides of a triangle BCD are a = 12 cm, b = 17 cm and c = 25 cm and altitude of a parallelogram is h.

Area of parallelogram, ABCD = 2(Area of triangle BCD)  ...(I)

Now, semi-perimeter(s) of triangle BCD will be:

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

= `(12 + 17 + 25)/2`

= `54/2`

= 27 cm

Area of triangle BCD = `sqrt(s(s - a)(s - b)(s - c))`  ...[By Heron’s formula]

= `sqrt(27(27 - 12)(27 - 17)(27 - 25))`

= `sqrt(27 xx 15 xx 10 xx 2)`

= `sqrt(9 xx 3 xx 3 xx 5 xx 5 xx 2 xx 2)`

= 3 × 3 × 5 × 2 cm²

= 90 cm²

So, area of parallelogram ABCD = 2 × Area of triangle BCD

 = 2 × 90 cm²

 = 180 cm²   ...(II)

As, Area of parallelogram ABCD = Base × Altitude

80 = DC × h

180 = 12 × h

h = `180/12`

h = 15 cm

Therefore, the area of parallelogram is 180 cm² and the length of altitude is 15 cm.