Page 273 - Start Up Mathematics_8 (Non CCE)

Here, a = 15 cm, b = 28 cm, c = 41 cm

abc++ 15 28 41+ + 84
s = = = = 42
2 2 2

Area of D SPA = ss as bs c( - )( - )( - )

= 42 42 15 42 28 42 41( - )( - )( - ) = 42 27 14¥ ¥ = 15 876, = 126 cm 2

2
2
Area of quadrilateral SNAP = 180 cm + 126 cm = 306 cm 2

EXERCISE 17.1
K 30 cm R
1. A paper is in the form of a rectangle DARK in which DA = 30 cm
and KD = 21 cm. A semicircular portion with AR as diameter is
cut-off. Find the area of the remaining part. 21 cm

D 30 cm A

A K S

2. Find the area of the shaded region, if PAST is a square of side
14 cm and ALS and PLT are semicircles. L

3. The length of a rectangular field is increased by 50% and its breadth
is decreased by 50% to form a new rectangular field. Find the M
percentage change in the area of the field. P T
4. A rectangle is 22 m long and 12 m wide. From its four corners, quadrants of radius 2.5 m have been
cut. Find the area of the remaining part.
5. The side of a square is 8 cm. Find the length of its diagonal.
6. The sides of two squares are in the ratio 4 : 5. Find the ratio of their areas.
7. How many tiles measuring 20 cm × 20 cm each will be required to pave a 1.5 m wide footpath around
a grassy plot of 25 m × 16 m?
8. The sides of a quadrilateral taken in order are 5 m, 12 m, 14 m and 15 m respectively. The angle
contained in the first two sides is a right angle. Find the area of the quadrilateral.
9. The adjacent sides of a parallelogram are 10 m and 8 m. If the distance between the longer sides is
4 m, find the distance between the shorter sides.

Area of a Trapezium
A trapezium is a quadrilateral in which one pair of opposite sides are parallel. Each of the two parallel sides
is called the base of the trapezium. The distance between the two parallel sides of the trapezium is called the
height of the trapezium (Fig. 17.9).
1 R A
Area of trapezium = × (Sum of lengths of parallel sides) × Height
2 h
1
= × (AR + ST) × h h
2
This formula is obtained by adding the areas of D RAS and D SAT. S N M T
\ Area of trapezium = Area of D RAS + Area of D SAT Fig. 17.9

265