AreaPage 1
1.  Find the area of a triangle whose sides measure 13 cm, 14 cm, and 15 cm ?  (a)80 cm²  (b)84 cm²  (c)86 cm ²  (d)88 cm² 

Answer is: BLet a = 13, b = 14, and c = 15.
Then, s = 1⁄2(a + b + c)
∴ s = 21
∴ (s  a) = 8, (s  b) = 7 and (s  c) = 6
∴ Area = √s(s  a) (s  b) (s  c)
Area = √21 x 8 x 7 x 6 = 84 cm².
2.  The base of rightangled triangle is 5 cm and its hypotenuse is 13 cm. Find its area ?  (a)28 cm²  (b)30 cm²  (c)32 cm²  (d)34 cm² 

Answer is: Bbase = 5 cm and hypotenuse = 13 cm.
Applying pythagoras theorem,
we find the third side of the triangle = √13²  5² = 12 cm
∴ Area of triangle = ½ x b x h
⇒ A = ½ x 5 x 12 = 30 cm²
3.  Find the area of an equilateral of side 3 cm ?  (a)9√3/4  (b)18√3/7  (c)7√3/4  (d)9√3/5 

Answer is: AArea of an equilateral triangle = √3a²/4
= √3 x 9/4 = 9√3/4 cm²
4.  The wheel of a motorcar makes 1000 revolutions in moving 550 m. Find the diameter of the wheel ?  (a)15.5  (b)16.5  (c)17.5  (d)18.5 

Answer is: CDistance covered = number of revolutions x circumference of the wheel.
⇒ 550 = 1000 x 22/7 x d (d = diameter of wheel)
∴ d = (550 x 7)/(1000 x 22) = 0.175 m
∴ d = 17.5 cm.
5.  A copper wire is bent in the shape of a square, enclosing an area of 272.25 cm². If the same wire is bent in the form of a circle, find the radius of the circle ?  (a)8.5 cm  (b)7.5 cm  (c)9.5 cm  (d)10.5 cm 

Answer is: DArea of square = 272.25 cm²
∴ side = √272.25 = 16.5 cm
Perimeter = 4 x 16.5 = 66 cm
This will be the circumference of the wheel
⇒ 2 x 22/7 x r = 66
∴ r = (66 x 7)/(2 x 22) = 10.5 cm.
6.  The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?  (a)16 cm  (b)18 cm  (c)22 cm  (d)24 cm 

Answer is: B2(l + b)/b = 5/1
2l + 2b = 5b
3b = 2l
b = (2/3) l
Then, Area = 216 cm
l x b = 216
l x (2/3) l = 216
l = 324
l = 18 cm.
7.  If the circumference of one circle is (3/2) times that of the other, how many times the area of the smaller one is the larger one ?  (a)4/9  (b)5/9  (c)9/5  (d)9/4 

Answer is: DLet the radius of smaller circle = r
⇒ Radius of bigger circle = 3r/2
Area of smaller circle = πr²
Area of bigger circle = 9πr²/4
∴ Ratio of area of bigger circle to that of smaller circle.
⇒ (9πr²/4)/(πr²) = 9/4
8.  A cow is tied to one corner of a square plot of side 14 m with a rope 10.5 m long. Find the area the cow can graze and also the area it cannot graze ?  (a)87.625 m² 108.375 m²  (b)84.625 m² 106.375 m²  (c)85.625 m² 110.375 m²  (d)86.625 m² 109.375 m² 

Answer is: DArea of square = 14 x 14 = 196 m²
The area that the cow can graze is a sector in the square and the radius of the sector is 10.5 m,
which is the length of the rope and angle of the sector is 90°.
Area of sector = (90/360) (22/7) (10.5 x 10.5) = 86.625 m²
Area that the cow cannot graze = 196 – 86.625 = 109.375 m².