Question

the area for trapezium is 405 centimetres square and the ratio of parallel sides is 4:5 and height is 18 centimetres find the actual length of the parallel sides.​

Answer 1

Given:

Area of the trapezium = 405cm²

ratio of parallel sides = 4:5

height of the trapezium = 18cm

To Find:

Actual length of the parallel sides

Solution:

Let the parallel side be 4x and 5x respectively

height = 18cm

the area of trapezium = 405cm²

⠀⠀$⟹ \frac{1}{2} h(a + b) = 405$

⠀⠀$⟹ \frac{1}{2} \times 18 \times (4x + 5x) = 405$

⠀⠀$⟹9 \times 9x = 405$

⠀⠀$⟹81x = 405$

$∴ \: x = \frac{405}{81} = 5$

➞actual Length of parallel side 1 = 4 × 5

${\boxed{\sf{\red{=\:20\:cm}}}}$

➞actual Length of parallel side 2 = 5 × 5

${\boxed{\sf{\red{=\:25\:cm}}}}$

Answer 2

Given :

• Area of Trapezium = 405 cm²
• Ratio of parallel sides is 4:5
• Height = 18 cm

To Find :

The actual length of parallel sides

Theory :

•Trapezium

It is defined as a shape with four sides and one set of parallel sides.

Types of Trapezium

1. Scalene
2. Right
3. and isosceles

Properties :

1. Sum of all the four angles of the trapezium = 360°
2. Diagonals intersect each other . etc

Area :

$\sf\:Area=\dfrac{1}{2}[sum\:of\:parallel\:sides]\times\:Height$

Solution :

Let the parallel sides of Trapezium be 4x and 5x

Diagram :

$\setlength{\unitlength}{15mm}\begin{picture}(6,6)\put(0,1){\line(1,0){2.5}}\put(2.5,1){\line(-2,5){0.6}}\put(0,1){\line(2,5){0.6}}\put(0.6,2.5){\line(1,0){1.3}}\put(0.6,1){\line(0,1){1.5}}\put(1.1,2.6){\sf{4x}}\put(1.1,0.8){\sf{5x}}\put(0.7,1.7){\sf{18 cm}}\end{picture}$

We know that

$\sf\implies\:A=\dfrac{1}{2}[sum\:of\:parallel\:sides]\times\:H$

Put the given values

$\sf\implies\:405=\dfrac{1}{2}\times(4x+5)\times\:18$

$\sf\implies\:405=\dfrac{18}{2}\times\:9x$

$\sf\implies\:405=9\times\:9x$

$\sf\implies\:405=81x$

$\sf\implies\:x=\dfrac{405}{81}$

$\sf\implies\:x=5$

Therefore, The length of of the parallel sides of Trapezium are 20 cm and 25 cm.