find the area of a trapezium whose parallel sides are 10cm and 25cm and non - parallel sides are 13 and 14 cm?
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Answer:
The parallel sides of a trapezium are 10 cm and 25 cm and non-parallel sides are 13 cm and 14 cm, find the area of the trapezium?
Area = 196 cm²
y + z + 10 = 25
y² + x² = 13²
z² + x² = 14²
Isolate y in the first equation: y = 15 - z
Replace y² in the second equation with (15 - z)
(15 - z)² + x² = 13²
Isolate x² in the 3rd equation: x² = 14² - z²
Replace x² in : (15 - z)² + x² = 13² : with 14² - z²
(15 - z)² + 14² - z² = 13² n: Multiply out (15 - z)²
225 - 30z - z² + 196 - z² = 169 : Simplify by combining z² and -z² as zero
225 - 30z + 196 = 169 : Simplify by combining 225 and 196 as 421
421 - 30z = 169 : isolate z by adding 30 z to both sides
421 = 30z + 169 : isolate z by subtracting 169 from both sides
252 = 30z : isolate z by dividing both sides by 30
z = 8.4
Now solve for x, the height, because you know z
x² = 14² - z²
x² = 196 - 8.4²
x² = 196 - 70.56
x² = 125.44 : Take the square root of both sides
x = 11.2
According to the diagram 11.2 seems very reasonable
Area of a trapezium = [(b₁ + b₂)•h]/2
Area = [(25 + 10)•11.2]/2 = 196 cm²
Area = 196 cm²
Answer:
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