# Heron's Formula

## Exercise 12.2 Part 2

Question 4: A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

**Answer:** Given; a = 26 cm, b = 28 cm and c = 30 cm, and based of parallelogram = 28 cm

For triangle: s = (26 + 28 + 30)/2 = 84/2 = 42

Area `=sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(42(42-26)(42-28)(42-30))`

`=sqrt(42xx16xx14xx12)`

`=sqrt(7xx2xx3xx4xx4xx2xx7xx2xx2xx3)`

`=sqrt(7^2xx3^2xx16^2)`

`=7xx3xx16=336 sq cm`

Area of parallelogram = base X height

Or, 336 = 28 X height

Or, Height = 336/28 = 12 cm

Question5: A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

**Answer:** Given; AB = BC = CD = AD = 30 cm and AC = 48 m

So, AO = 24 m

In ΔAOB; `BO^2 = AB^2 - AO^2`

`= 30^2 - 24^2`

`= 900 – 576 = 324`

Or, `BO = 18 m`

So, second diagonal of rhombus `= 18 xx 2 = 36 m`

Area of Rhombus `= ½ xx d_1 xx d_2`

`= ½ xx 48 xx 36 = 864 sq m`

So, area for each cow `= 864/18 = 48 sq m`

Question 6: An umbrella is made by stitching 10 triangular pieces of cloth of two different colours, each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

**Answer:** a = 20 cm, b = 50 cm, c= 50 cm

So, `s = (20 + 50 + 50)/2 = 60`

Area `=sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(60(60-50)(60-50)(60-20))`

`=sqrt(60xx10xx10xx40)`

`=sqrt(10^4xx2^2xx6)=200sqrt6 sq cm`

Cloth of each colour `= 10 xx 200sqrt6 sq cm`