Question

parallel sides of a trapezium are 60m and 75m and its non parallel sides are 9m and 12m find its height and area.

Answer 1

here is the answer full solution but diagram is some error so don't worry

Answer 2

Answer:

The height of Trapezium is 7.2 meters and

The Area of Trapezium is  486 m²  .

Step-by-step explanation:

Given as :

The measure of parallel sides of Trapezium are 60 m , 75 m

The measure of non-parallel side of Trapezium are 9 m , 12 m

Now, From figure

The measure of side AB = 75 m

The measure of side BC = 12 m

The measure of side CD = 60 m

The measure of side DA = 9 m

Now, after construction

Line DA parallel line OC

So, The measure of side OC = DA = 9 m

From Triangle BOC , right angle at O

OC² + BC² = BO²

Or, 9² + 12² = BO²

Or, 225 =  BO²

∴ BO = $\sqrt{225}$ = 15 m

Now, Area of Triangle BOC = x

From Heron's formula

Area = $\sqrt{s(s - a) (s-b) (s-c)}$

where s = $\dfrac{a+b+c}{2}$

and , a = 9 m, , b = 12 m , c = 15 m

So, s  =  $\dfrac{9+12+15}{2}$

Or, s = 18 m

So, Area = $\sqrt{18\times (18-9)\times (18-12)\times (18-15)}$

or, x = $\sqrt{18\times 9\times 6\times 3}$

∴  x = $\sqrt{2916}$

i.e x = 54 m²

Now, Again ,

From The Area of Triangle BOC

Area = $\dfrac{1}{2}$  × base × height

Or, 54 m² =  $\dfrac{1}{2}$  × BO × H

Or, 54 m² =  $\dfrac{1}{2}$  × 15 × H

Or, 54 × 2 = 15 × H

Or, 15 × H = 108

∴  H = $\dfrac{108}{15}$

i.e Height of Trapezium = H = 7.2 m

now, again

From The Area of Trapezium

Area of Trapezium =  $\dfrac{1}{2}$  × (sum of opposite sides) × Height

Or, Area of Trapezium =  $\dfrac{1}{2}$  × (CD + AB) × H

Or, Area of Trapezium =  $\dfrac{1}{2}$  × (60 m + 75 m) × 7.2 m

Or, Area of Trapezium =  $\dfrac{1}{2}$  × (135 m) × 7.2 m

Or, Area of Trapezium = 486 m²

Hence, The height of Trapezium is 7.2 meters and The Area of Trapezium is  486 m²  . Answer