Question

One of the two parrallel sides of a trapezium is one half of the other if the height of the trapezium is 7cm and the area is 5.5cm² calculate the length of the parallel sides

Answer 1

Given :

• height of trapezium = 7cm
• area of trapezium = 5.5 cm²

To find :

• length of the parallel sides

Formula used :

$\sf a = \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times h$

where :-

• a = area of trapezium
• h = height

Solution :

One of the two parrallel sides of a trapezium is one half of the other.

In the diagram ( refer attachment) :-

• AB and CD are parallel to each other.

Let CD = 2x

therefore, AB = x

$\sf \implies 5.5 = \dfrac{1}{2} \times (x + 2x) \times 7$

$\sf \implies 5.5 \times 2 = (x + 2x) \times 7$

$\sf \implies 11= (3x) \times 7$

$\sf \implies 11= 21x$

$\sf \implies \dfrac{11}{21} = x$

Now , AB = 11/21 cm

CD = 2× (11/21) = 22/21 cm

Answer :

$\sf \: length \: of \: the \: parallel \: sides = \dfrac{11}{21} \: cm \: and \: \dfrac{22}{21} \: cm$

Answer 2

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

Trapezium's

• Height = 7cm
• Area = 5.5 ${\sf {{cm}^{2}}}$

$\bf\purple{\underline {To\:Find-}}$

• The length of the parallel sides

$\bf\pink{\underline {Solution:-}}$

Let the one side be 'x' and the other side be '2x' from the parallel sides.

∴Sum of the parallel sides = 2x + x = 3x

We know that,

✷ A = ½ x (sum of the parallel sides) × h

here,

• A = Area of Trapezium
• h = height of the Trapezium

∴ 5.5 = ½ × (x + 2x) × 7

⇢ 5.5 ×2 = (x + 2x) × 7

⇢ 11 = 3x × 7

⇢ 11 = 21 x

⇢ x = ${\sf { \frac{11}{21} }}$

Hence, one side is = x = ${\sf { \frac{11}{21} }}$

The other side is = 2x = ${\sf { \frac{11×2}{21} }}$ = ${\sf { \frac{22}{21} }}$

${\sf\green {\therefore {The \:length \:of \:the\: parallel\: sides\: are\: \frac{11}{21} cm\: and \frac{22}{21} cm}}}$

_______________________________

$\bf\orange{\underline {Important\:Formulas:-}}$

• Area of Square = $\sf{(one \: side)}^{2}$
• Area of Parallelogram = base × height
• Area of Rectangle = breadth × length
• Area of Rhombus = base × height
• Area of Parallelogram = $\sf{ \frac{1}{2} \times d_{1} \times d_{2}}$ (where 'd' = diagonal)