Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.
Answers
Given :Two parallel sides of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm.
Let ABCD is a trapezium in which AB = 77 cm, BC = 26 cm, CD = 60 cm, DA = 25 cm
Draw CE || AD
Now, ACDE is a parallelogram
BE = AB - DC = 77- 60 = 17 cm
In ∆BEC,
Let a = 25 cm , b = 17 cm and c = 26 cm
Semi perimeter of Δ (s) = (a + b + c)/2
s = (a + b + c)/2
s = (25 + 17 + 26)/2
s = 68/2
s = 34 cm
By using Heron's formula :
Area of Δ , A = s√(s − a)(s − b)(s − c)
A = √34(34 - 25) (34 - 17) (34 - 26)
A = √34 × 9 × 17 × 8
A = √(2 × 17) × (3 × 3) × 17 × (2 × 4)
A = √(2 × 2) × ( 17 × 17) × (3 × 3) × 4
A = 2 × 17 × 3 × 2
A = 34 × 6
Area of Δ , A = 204 cm²
Therefore area of ∆BCE = ½ × base × altitude
204 = ½ × Altitude
204 × 2 = 17× Altitude
Altitude = (204 × 2)/17
Altitude = 12 × 2
Altitude = 24 cm
Area of trapezium ABCD = ½ (sum of parallel sides) × altitude
Area of trapezium ABCD = ½ (DC + AB) × altitude
Area of trapezium ABCD = ½ (60 + 77) × 24
Area of trapezium ABCD = 12 × 137
Area of trapezium ABCD = 1644 cm²
Hence, the area of trapezium ABCD is 1644 cm².
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