Page 1 - LA-2

SAI International School
CLASS - VIII

Mathematics
CHAPTER-11 :Mensuration Lesson Notes-2

SUBTOPICS: Area of trapezium and general quadrilateral

Area of Trapezium
A trapezium is a quadrilateral that has only one pair of parallel sides.

Area of a trapezium = half of the sum of the lengths of parallel sides * perpendicular
distance between them.

= (1/2) * (a + b) * h

Where a and b are the opposite sides of the trapezium, which are parallel and h is
the perpendicular height of the trapezium.

2
Example : The area of a trapezium is 34 cm and the length of one of the parallel
sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.
Solution: Let the length of the other parallel side be b.
Length of one parallel side (a) = 10 am and height (h) = 4 cm
Area of trapezium = 1/2 * (a + b) * h
=> 34 = 1/2 * (10 + b) * 4
=> 34 = (10 + b) * 2
=> 10 + b = 34/2
=> 10 + b = 17
=> b = 17 – 10
=> b = 7
Hence, another required parallel side is 7 cm.

Area of a General Quadrilateral
To find the area of a quadrilateral, we can split it into two triangles by drawing one of
its diagonals as shown in the given
figure.

Now, area of quadrilateral ABCD = (area of Δ ABC) + (area of Δ ADC)

= (1/2) * AC * h1 + (1/2) * AC * h2
= (1/2) * AC * (h1 + h2)
= (1/2) * d * (h1 + h2)

where d denotes the length of diagonal AC.

1