Two parallel sides of a trapezium are 120 cm and 154 cm. The other two sides are 50 cm and 52 cm each. Find the area of the trapezium.
Answers
Step-by-step explanation:
Let ABCD be the trapezium such that AB and CD are parallel, witj AB = 120 cm. BC = 52 cm, CD = 154 cm and DA = 50 cm. ... So area of trapezium ABCD = (120+154)*48/2 = 274*24 = 6576 sq cm.
ANSWER:
Area = 6576 cm²
GIVEN:
b₁ = 120 cm
b₂ = 154 cm
OTHER SIDES = 50 cm, 52 cm
TO FIND:
AREA OF THE TRAPEZIUM.
FORMULA:
Area of a trapezium = ((b₁ + b₂) × h)) / 2
EXPLANATION:
y + z + 120 = 154
From Pythagoras theorem:
y² + x² = 50²
z² + x² = 52²
Substitute y = 34 - z in y² + x² = 50²
(34 - z)² + x² = 50²
Substitute x² = 52² - z² in (34 - z)² + x² = 50²
(34 - z)² + 52² - z² = 50²
1156 - 68z + z² - z² + 2704 = 2500
1156 - 68z + 2704 = 2500
3860 - 68z = 2500
3860 = 68z + 2500
68z = 3860 - 2500
68z = 1360
z = 20
Substitute z = 20 in x² = 52² - z²
x² = 2704 - 20²
x² = 2704 - 400
x² = 2304
x = 48
Area = ((120 + 154) × 48) / 2
Area = (274 × 48) / 2
Area = 274 × 24
Area = 6576 cm²
Area of the trapezium = 6576 cm².
NOTE : DIAGRAM IN ATTACHMENT.
