Question

A field is in the form of a trapezium whose parallel sides are 150 m and 200 m respectively. If the distance between the parallel sides is 50 m, then the area of the field is?​

Answer 1

Given :

• 1st Parallel Side = 150 m
• 2nd Parallel Side = 200 m
• Distance between them = 50 m

To Find :

• Find the Area

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Trapezium)}} = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height }}}}}$

Where :

• a = 1st Parallel Side
• b = 2nd Parallel Side

$\dag$ Calculating the Area :

${\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height }}}} \\ \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times \bigg( 150 + 200 \bigg) \times 50 }}}} \\ \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times 350 \times 50 }}}} \\ \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times 17500 }}}} \\ \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \dfrac{17500}{2} }}}} \\ \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = \cancel\dfrac{17500}{2} }}}} \\ \\ \\ \\ \ {\qquad \; \; {\dashrightarrow \; {\pmb{\underline{\boxed{\pink{\frak{ Area = 8750 \; {m}^{2} }}}}}}}}$

$\therefore \;$ Area of the Trapezium field is 8750 m² .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

Given:-

• 1st parallel side
• 2nd parallel side
• Distance between parallel sides

Also given that:-

• 1st parallel side=150m
• 2nd parallel side=200m
• Distance between them=50m

Formula used:-

$\large \blue{\underline{ \green{ \boxed{\sf{ \pink{ \implies \red{\frac{1}{2} \times (a + b) \times h = area}}}}}}}$

Where,

• a= 1st parallel side
• b= 2nd parallel side
• h= Distance between the parallel sides.
• a= Area of trapezium.

Solution:-

We have a trapezium with different units and we have to find the area of the trapezium.As all the values are given we can simply put the values and get the result.

On calculating we get:-

$\large\underline{\sf{ \implies \frac{1}{2} \times (150m + 200m) \times 50m }}$

$\large\underline{\sf{ \implies \frac{1}{2} \times 350m \times 50m }}$

$\large\underline{\sf{ \implies 8750 {m}^{2} }}$

______________________________________

Extra information!!

• A trapezium is a 2-Dimensional(2-D) figure.
• It is a quadrilateral with two sides parallel and two sides non parallel.
• To calculate the area of trapezium we have to find it's Two parallel sides and the distance between the two parallel sides.
• Formula to calculate area of trapezium is 1/2× (a+b) ×h.
• To calculate the perimeter of trapezium we need it's all sides.
• Formula to calculate perimeter is Sum of all sides.