The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium
Solution:
Area of a Trapezium = (½) × (Sum of a Parallel Sides) × Height (1)
In the above diagram of the trapezium the parallel sides are AB (40 cm) and DC(20 cm)
The height of the Trapezium MC needs to be determined.
From point C a line LC is drawn parallel to AD
LC = AD = BC
Hence △BLC is an isosceles triangle and the perpendicular MC is also the median and hence bisector of LB.
Also,
AL = LB = 20
MB = 10
Therefore,
MC² = BC² - MB²
(MC)² = (26)² - (10)²
(MC)² = 676 - 100
(MC)² = 576
MC = 24 cm Height of Trapezium
Therefore Area of Trapezium can be calculated by using equation (1)
Area of a Trapezium = (1/2) × (40 + 20) × 24
Area of Trapezium = (1/2) × 60 × 24 = 720 cm²
✦Try This: The parallel sides of a trapezium are 20 cm and 10 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.
Area of a Trapezium = (1/2) × (Sum of a Parallel Sides) × Height (1)
In the above diagram of the trapezium the parallel sides are AB (40 cm) and DC(20 cm)
The height of the Trapezium MC needs to be determined.
From point C a line LC is drawn parallel to AD
LC = AD = BC
Hence △BLC is an isosceles triangle and the perpendicular MC is also the median and hence bisector of LB.
Also,
AL = LB = 10
MB = 5
Therefore,
MC² = BC² - MB²
(MC)² = (13)² - (5)²
(MC)² = 169 - 25
(MC)² = 144
MC = 12 cm Height of Trapezium
Therefore Area of Trapezium can be calculated by using equation (1)
Area of a Trapezium = (1/2) × (20 + 10) × 12
Area of Trapezium = (1/2) × 30 × 12 = 180 cm²
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Sample Problem 9
The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium
Summary:
The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, the area of the trapezium is 720 cm²
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