two parallel sides of the trapezium are 60 cm and 77 cm and the other sides are 25 cm and 26 cm.Find the area of the trapezium
Answers
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.