Question

PQRS is a trapezium in which PQ is parallel to SR. If PQ=12cm,SR=5cm and the area of the trapezium is 119cm²,calculate the height of the trapezium

Answer 1

$\huge{\orange{\underline{\underline{ANSWER}}}}$

Given :

PQRS is a trapezium .

PQ is parallel to SR . ( PQ || SR)

Area of the Trapezium = 119 cm².

$\rule{400}{2}$

Required to find :

1. Height of the Trapezium.

$\rule{400}{2}$

Formula used :

$\blue{\boxed{\red{Area\;of\; the\; Trapezium\; = \dfrac{1}{2} \times h \times (a + b)}}}$

$\rule{400}{2}$

Explanation :

$\rule{250}{1}$

What is a Trapezium ?

A Trapezium is a type of quadrilateral in which one pair of opposite sides are equal .

The parallel sides are called as the bases and the unparallel sides are called as the legs .

A Trapezium is also known as Trapezoid .

$\rule{250}{1}$

Types of trapezium ;

1. Right angled Trapezium :

A Trapezium is said to be right angled if it has 2 right angles .

2. Isosceles Trapezium :

A Trapezium in which the unparallel sides are equal .

3. Scalene Trapezium :

A Trapezium in which no angles , no sides are equal to one another .

$\rule{250}{1}$

Formula related to Trapezium :

$\rightarrow{Area \:of \; the \: Trapezium \:= \dfrac{1}{2} \times h \times (a + b)}$

Here,

h is the distance between the parallel . simply we can say that it is the height of the Trapezium .

a,b are the length of the parallel sides .

$\Rightarrow{Perimeter \: of\: the\: Trapezium\: = Side a + side b + side c + side d }$

Knowing this content is important .

Now, let's crack the above question .

$\rule{400}{2}$

Solution :

Given values :

• PQ (a) = 12cm
• SR (b) = 5 cm
• Area of the Trapezium = 119 cm²

Distance between the parallel sides = Height of the Trapezium

Let the height of the Trapezium be " x " cm .

Formula

$\boxed{Area \;of \;the \;Trapezium \;= \dfrac{1}{2} \times h \times (a + b)}$

Now substitute the values in the formula .

$\longrightarrow{119 {cm}^{2} = \dfrac{1}{2} \times x \times ( 12 + 5 )}$

$\longrightarrow{ 119 = \dfrac{1}{2} \times x \times 17}$

$\longrightarrow{ 119 = \dfrac{1}{2} \times 17x }$

Transpose the 2 from R.H.S. to L.H.S.

$\longrightarrow{ 119 \times 2 = 17x }$

$\longrightarrow{ 238 = 17x}$

..... Exchange the numbers on both sides ...

$\Rightarrow{ 17x = 238 }$

$\Rightarrow{ x = \dfrac{238}{17}}$

$\implies{ x = 14 cm }$

Hence,

$\rightarrow{\boxed{\therefore{Height\:of\:the\: Trapezium\: = x = 14cm}}}$

$\rule{400}{2}$

✅ Hence Solved ..