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If measurements of Shazia’s plot are as follows: YM = 10 m, WL = 6 m, LM = 12 m, MX = 4 m.
1
Thus, the area of Shazia’s plot will be × 10 × (22 + 12) sq. m = 170 sq. m.
2 [Q a = c + b + d = 6 m + 12 m + 4 m = 22 m]

2
Example 6: The area of a trapezium is 119 m and the distance between its parallel sides is 7 m. If
one of the parallel sides is longer than the other by 10 m, find the two parallel sides of the trapezium.

2
Solution: Given that the area of the trapezium = 119 m and the distance between two parallel
sides (height) = 7 m.
Let the length of the shorter parallel side be x m.
Then, the length of the longer parallel side will be (x + 10) m.

1
We have, area of a trapezium = × Height × (Sum of parallel sides)
2
2
⇒ 119 m = 1 × 7 m × (x + x + 10) m
2
×
 119 2
⇒   7  = (2x + 10) Think and Answer

⇒ 34 = (2x + 10) A parallelogram is divided

⇒ 34 – 10 = 2x into two congruent triangles by drawing
a diagonal across it. Can we divide a
⇒ 24 = 2x ⇒ x = 12 trapezium into two congruent triangles?

So, x = 12 m and (x + 10) m = (12 + 10) m = 22 m
Thus, the parallel sides of the trapezium are 12 m and 22 m.

Area of a General Quadrilateral

A general quadrilateral can be split into two triangles by drawing one of its diagonals. In that case,
the area of the quadrilateral is equal to the sum of the areas of the two triangles.
Let ABCD be a quadrilateral. In the quadrilateral ABCD, BD is one of its diagonals that divides
quadrilateral ABCD into two triangles, ABD and BCD. Further, let AE = h and CF = h be the
2
1
altitudes on BD.
\ Area of quadrilateral ABCD = Area of DABD + Area of DBCD
A
1 1
= × BD × AE + × BD × FC h 1
2 2
1 1 D F E B
= × BD × h + × BD × h 2
1
2 2 h 2
1
= × BD ×(h + h ) C
1
2
2
Since, BD is the diagonal of the given quadrilateral ABCD. If we take BD = d, then,
1
area of a quadrilateral = × d ×(h + h )
2
1
2
1
Thus, the area of a quadrilateral = × length of diagonal × (sum of the lengths of the perpendiculars
2
from the other two vertices on it).

235 Mensuration