Question

1. Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm
2. Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them is 16 cm.
3. The area of a trapezium is 1080 cm². If the lengths of its parallel sides are 55.6 cm and 34.4 cm, find the distance between them.
4. The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, find the other.
5. The area of a trapezium is 180 cm² and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the two parallel sides.

Answer 1

1]area of trapezium = 1/2 * distance between two parallel sides * ( sum of two parallel sides)

therefore here

area = 1/2 * 15 * (24+20)

= 1/2 * 15 * 44

= 22 *15

330 sqcm

2]given the Length one of the parallel side of the trapezium is 38.7cm and and the other parallel side is 22.3cm.

given height is 16cm.

area of the trapezium = 1/2×h(b1+b2)

= 1/2×16(38.7+22.3)

= 8×61

= 488cm²

3] Area of a trapezium= (1/2*sum of parallel sides*height)

Let the distance between them be x

1080cm^2= (1/2*(34.4cm+55.6cm)*x)

x= 12cm

Ans= 12cm

4] area of trapezium = 1586 cm²

(1/2) × (sum of parallel sides) × height = 1586 cm²

1/2 × (84+other side) × 26 = 1586 cm²

84+other side = (1586×2)/26

84+other side = 112

other side = 122-84 = 38 cm

5] height of trapezium =9 cm

one of other side of trapezium is longer than 6 cm

one is 6cm and other is x+6

Area of trapezium =

1÷2 (sum of parallel sides )×height

1÷2 ( x + x+6) ×9 =180

1÷2 (2x+6)×9= 180

x+3×9=180

x+3=180÷9

x+3=20

x=20-3

x=17

one side is x = 17 cm

other side x+6 =17+6=23cm

please mark me the brainliest

Answer 2

Solution 1:

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

Trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The area of trapezium.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Formula use :

$\bf{\boxed{\bf{Area\:of\:trap.=\frac{1}{2} \times(sum\:of\:base)\times height}}}}}$

A/q

$\implies\tt{Area\:of\:trap.=\dfrac{1}{2} \times (24cm+20cm)\times 15cm}\\\\\\\implies\tt{Area\:of\:trap.=\dfrac{1}{\cancel{2}} \times \cancel{44cm}\times 15cm}\\\\\\\implies\tt{Area\:of\:trap.=(22\times 15)cm^{2} }\\\\\\\implies\tt{\pink{Area\:of\:trap.=330cm^{2}}}$

Solution 2:

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

Trapezium whose parallel sides are 38.7 cm and 22.3 cm and the distance between them is 16 cm.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The area of trapezium.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

$\implies\tt{Area\:of\:trap.=\dfrac{1}{2} \times (38.7cm+22.3cm)\times 16cm}\\\\\\\implies\tt{Area\:of\:trap.=\dfrac{1}{\cancel{2}} \times 61cm\times \cancel{16cm}}\\\\\\\implies\tt{Area\:of\:trap.=(61\times 8)cm^{2} }\\\\\\\implies\tt{\pink{Area\:of\:trap.=488cm^{2}}}$

Solution 3:

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

The area of a trapezium is 1080 cm². If the length of its parallel sides are 55.6 cm and 34.4 cm.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The distance between them.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the height of trapezium be r cm

We know that formula of the area of trapezium :

$\mapsto\sf{\green{Area\:of\:trapezium=\dfrac{1}{2} \times (sum\:of\:base)\times height}}\\\\\\\mapsto\sf{1080cm^{2} =\dfrac{1}{2} \times (55.6+34.4)cm\times r}\\\\\\\mapsto\sf{1080cm^{2} =\dfrac{1}{\cancel{2}} \times \cancel{90cm}\times r}\\\\\\\mapsto\sf{1080cm^{2} =45cm\times r}\\\\\\\mapsto\sf{r=\cancel{\dfrac{1080cm^{2} }{45cm} }}\\\\\\\mapsto\sf{\pink{r=24\:cm}}$

∴ The height of trapezium is r = 24 cm .

Solution 4:

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

The area of trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The other parallel sides.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

let the other parallel sides be r cm

$\mapsto\sf{\green{Area\:of\:trapezium=\dfrac{1}{2} \times (sum\:of\:base)\times height}}\\\\\\\mapsto\sf{1586cm^{2} =\dfrac{1}{\cancel{2}} \times (84+r)cm\times \cancel{26cm}}\\\\\\\mapsto\sf{1586cm^{2} =(84+r)cm\times 13cm}\\\\\\\mapsto\sf{84cm+r=\cancel{\dfrac{1586cm^{2} }{13cm} }}\\\\\\\mapsto\sf{84cm+r=122cm}\\\\\\\mapsto\sf{r=122cm-84cm}\\\\\\\mapsto\sf{\pink{r=38\:cm}}$

∴ The other parallel sides is r = 38 cm .

Solution 5:

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

The area of a trapezium is 180 cm² and it;s height is 9 cm. If one of the parallel sides is longer than the other by 6 cm.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The two parallel sides.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Formula use :

$\bf{\boxed{\sf{Area\:of\:trapezium=\frac{1}{2} \times (sum\:of\:base)\times height}}}}}$

Let the length of one parallel sides be r cm

Let the length of other parallel sides be (r+6) cm

A/q

$\implies\sf{180cm^{2} =\dfrac{1}{2} \times [r+(r+6)]\times 9cm}\\\\\\\implies\sf{180cm^{2} =\dfrac{1}{2} \times (r+r+6)\times 9cm}\\\\\\\implies\sf{360cm^{2} =2r+6\times 9cm}\\\\\\\implies\sf{2r+6=\cancel{\dfrac{360cm^{2} }{9cm} }}\\\\\\\implies\sf{2r+6=40cm}\\\\\\\implies\sf{2r=(40-6)cm}\\\\\\\implies\sf{2r=34cm}\\\\\\\implies\sf{r=\cancel{\dfrac{34}{2} }}\\\\\\\implies\sf{\pink{r=17\:cm}}$

Thus;

$\underbrace{\sf{The\:one\:parallel\:side\:=r=17\:cm}}}}}\\\underbrace{\sf{The\:other\:parallel\:side\:=(r+6)=(17+6)cm=23\:cm}}}}}$