Question : A field is in the shape of a trapezium whose parallel sides are 200 m and 400 m long, whereas each of the other two sides is 260 m long. What is the area (in m2) of the field?
Option 1: 72000
Option 2: 52000
Option 3: 48000
Option 4: 60000
Correct Answer: 72000
Solution :
ABDC is a trapezium AB = 200 m, CD = 400 m, AC = BD = 260 m AB = EF = 200 m and CE = FD ⇒ CD = CE + EF + FD ⇒ 400 = CE + 200 + DF In isosceles trapezium CE = FD ⇒ 2CE = 400 – 200 = 200 ⇒ CE = 100 m In triangle BFD, BC2 = BF2 + FD2 ⇒ (260)2 = BF2 + (100)2 ⇒ BF2 = 67600 – 10000 = 57600 ⇒ BF2 = 57600 ⇒ BF = 240 m Area of trapezium = $\frac{1}{2}$ × (Sum of parallel side) × (Distance between parallel side) Area of trapezium = $\frac{1}{2}$ × (400 + 200) × 240 = 120 × 600 = 72000 m2 Hence, the correct answer is 72000.
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Question : The two parallel sides of a trapezium are 17 cm and 15 cm, respectively. If the height of the trapezium is 6 cm, then its area (in m2) is:
Option 1: 9.6
Option 2: 960
Option 3: 0.96
Option 4: 0.0096
Question : The two parallel sides of a trapezium are 27 cm and 13 cm respectively. If the height of the trapezium is 8, then what is its area in m2?
Option 1: 0.032
Option 2: 0.056
Option 3: 0.016
Option 4: 0.32
Question : The two parallel sides of a trapezium are 27 cm and 13 cm, respectively. If the height of the trapezium is 7 cm, then what is its area in m2?
Option 1: 1.4
Option 2: 0.014
Option 3: 140
Option 4: 0.14
Question : What will be the area of a plot of quadrilateral shape, one of whose diagonals is 20 m and lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively?
Option 1: 400 m2
Option 2: 250 m2
Option 3: 200 m2
Option 4: 300 m2
Question : The area of a trapezium-shaped field is 1785 square feet. The distance between the two parallel sides is 35 feet and one of the parallel sides is 42 feet long. What is the length of the other parallel side?
Option 1: 60 feet
Option 2: 35 feet
Option 3: 40 feet
Option 4: 65 feet
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