Question

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

Answer 1

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}

225

= 15 m

Now, Area of Triangle BOC = x

From Heron's formula

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

s(s−a)(s−b)(s−c)

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

2

a+b+c

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

So, s = \dfrac{9+12+15}{2}

2

9+12+15

Or, s = 18 m

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

18×(18−9)×(18−12)×(18−15)

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

18×9×6×3

∴ x = \sqrt{2916}

2916

i.e x = 54 m²

Now, Again ,

From The Area of Triangle BOC

Area = \dfrac{1}{2}

2

1

× base × height

Or, 54 m² = \dfrac{1}{2}

2

1

× BO × H

Or, 54 m² = \dfrac{1}{2}

2

1

× 15 × H

Or, 54 × 2 = 15 × H

Or, 15 × H = 108

∴ H = \dfrac{108}{15}

15

108

i.e Height of Trapezium = H = 7.2 m

now, again

From The Area of Trapezium

Area of Trapezium = \dfrac{1}{2}

2

1

× (sum of opposite sides) × Height

Or, Area of Trapezium = \dfrac{1}{2}

2

1

× (CD + AB) × H

Or, Area of Trapezium = \dfrac{1}{2}

2

1

× (60 m + 75 m) × 7.2 m

Or, Area of Trapezium = \dfrac{1}{2}

2

1

× (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 .

Hope it helps you....

Answer 2

Answer:

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}

225

= 15 m

Now, Area of Triangle BOC = x

From Heron's formula

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

s(s−a)(s−b)(s−c)

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

2

a+b+c

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

So, s = \dfrac{9+12+15}{2}

2

9+12+15

Or, s = 18 m

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

18×(18−9)×(18−12)×(18−15)

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

18×9×6×3

∴ x = \sqrt{2916}

2916

i.e x = 54 m²

Now, Again ,

From The Area of Triangle BOC

Area = \dfrac{1}{2}

2

1

× base × height

Or, 54 m² = \dfrac{1}{2}

2

1

× BO × H

Or, 54 m² = \dfrac{1}{2}

2

1

× 15 × H

Or, 54 × 2 = 15 × H

Or, 15 × H = 108

∴ H = \dfrac{108}{15}

15

108

i.e Height of Trapezium = H = 7.2 m

now, again

From The Area of Trapezium

Area of Trapezium = \dfrac{1}{2}

2

1

× (sum of opposite sides) × Height

Or, Area of Trapezium = \dfrac{1}{2}

2

1

× (CD + AB) × H

Or, Area of Trapezium = \dfrac{1}{2}

2

1

× (60 m + 75 m) × 7.2 m

Or, Area of Trapezium = \dfrac{1}{2}

2

1

× (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

Step-by-step explanation:

hope this helps you................