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.
Answers
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:
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.
