Question

The area of a trapezium is 594 sq. cm. Its parallel sides are in the ratio 4 : 5 The height of the
trapezium is 12 cm. Find the length of the sides.​

Answer 1

Given :

• Area of Trapezium is 594 cm² .
• Parallel Sides are in the ratio 4:5 .
• Height of Trapezium is 12 cm .

To Find :

• Length of Parallel Sides .

Solution :

$\longmapsto\tt{Let\:one\:parallel\:Side\:be=4x}$

$\longmapsto\tt{Let\:other\:parallel\:Side\:be=5x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:Sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{594=\dfrac{1}{{\cancel{2}}}\times{(4x+5x)}\times{{\cancel{12}}}}$

$\longmapsto\tt{594=4x+5x\times{6}}$

$\longmapsto\tt{594=9x\times{6}}$

$\longmapsto\tt{\cancel\dfrac{594}{6}=9x}$

$\longmapsto\tt{99=9x}$

$\longmapsto\tt{\cancel\dfrac{99}{9}=x}$

$\longmapsto\tt\bf{11=x}$

Value of x is 11 .

Therefore :

$\longmapsto\tt{Length\:of\:one\:parallel\:Side=4(11)}$

$\longmapsto\tt\bf{44\:cm}$

$\longmapsto\tt{Length\:of\:other\:parallel\:Side=5(11)}$

$\longmapsto\tt\bf{55\:cm}$

_______________________

VERIFICATION :

$\longmapsto\tt{594=\dfrac{1}{2}\times{4x+5x}\times{12}}$

$\longmapsto\tt{594=\dfrac{1}{2}\times{4(11)+5(11)}\times{12}}$

$\longmapsto\tt{594=\dfrac{1}{{\cancel{2}}}\times{(44+55)}\times{{\cancel{12}}}}$

$\longmapsto\tt{594=99\times{6}}$

$\longmapsto\tt\bf{594=594}$

HENCE VERIFIED

Answer 2

Step-by-step explanation:

Given :

• The area of a trapezium is 594 sq. cm.

• Its parallel sides are in the ratio 4 : 5.

• The height of the trapezium is 12 cm.

To Find :

• Find the length of the sides.

Solution :

The area of a trapzoid is given by :

Let the length of the parallel sides be 4x and 5x.

Sum of parallel sides = 4x + 5x

Sum of parallel sides = 9x

Concept :

Explanation:

• In order to find the area of an isoceles trapezoid, you must average the bases and multiply by the height. In order to find the height, you must draw an altitude. This creates a right triangle in which one of the legs is also the height of the trapezoid.

A = 1/2 (Sum of parallel sides) × height

Put all values in formula :

594 = 1/2 ( 9x ) × 12

1/2 × 12 When 1/2 multiplied by 12 is equal to 6

594 = 9x × 6

594 = 54 x

x = 594/ 54

x = 11

Sides of trapzoid = 4( x )

Sides of trapzoid = 4 × 11

Sides of trapzoid = 44

Sides of trapzoid = 5( x )

Sides of trapzoid = 5 × 11

Sides of trapzoid = 5 cm.

Hence, The length of the sides are 44 cm and 55 cm.

More to know :

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezium in English outside North America, but as a trapezoid in American and Canadian English.

• Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

Perimeter: sum of lengths of sides of trapezoid