Question

In a trapezium, the parallel sides measure 40 cm and 20 cm. Calculate the area of the trapezium if its non-parallel sides are equal having the lengths of 26 cm.​

Answer 1

Area of trapezium = 1/2 x ( sum of parallel sides) x height

Area = 1/2 x (40+20) x 26

Area = 1/2 x 60 x 26

Area = 60 x 23

Area = 1380 m^2

Answer 2

Answer:

Area of trapezium = 720cm²

Step-by-step explanation:

From the question statement draw the diagram.

• Consider a trapezium of ABCD. Let AB and DC be the parallel sides as shown in the figure. [ See Figure (1 )]

Now, CM will be the distance between the two parallel sides or the height of the trapezium.

We know,

Area of trapezium = ½ × sum of parallel sides × height.

So, height has to be found.

In the diagram, draw CL || AD

[ See Figure (2) ]

Now, ALCD is a parallelogram ⇒ AL = CD = 20 cm and CL = AD = 26 cm

As AD = CB,

CL = CB ⇒ ΔCLB is an isosceles triangle with CB as its height.

⇒Here, BL = AB – AL = (40 – 20) = 20 cm. So,

⇒LM = MB = ½ BL = ½ × 20 = 10 cm

Now, in ΔCLM,

⇒CL² = CM² + LM² (Pythagoras Theorem)

⇒26² = CM² + 10²

⇒CM² = 26² – 10²

Using algebraic identities, we get;

⇒ 26² – 10² = (26 – 10) (26 + 10)

Hence,

⇒CM² = (26 – 10) (26 + 10) = 16 × 36 = 576

⇒CM = √576 = 24 cm

Now, the area of trapezium can be calculated.

Area of trapezium, ABCD = ½ × (AB + CD) × CM

⇒Area of trapezium = ½ × (20 + 40) × 24

⇒ Area of trapezium ABCD = 720 cm².