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Q:

The area of a circle of radius 5 is numerically what percent its circumference?

A) 150%	B) 250%
C) 350%	D) 450%

Answer & Explanation Answer: B) 250%

Explanation:

required percentage = $\frac{{πr}^{2}}{2 πr} \times 100 = 250$ %

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Q:

The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:

A) 75	B) 85
C) 95	D) 105

Answer & Explanation Answer: A) 75

Explanation:

Area of field = $\frac{1}{2} * (5 x + 3 x) * 24$ = 96x sq.m

96x = 1440 => x = $\frac{1440}{96}$ = 15

Hence, the length of longer parallel side = 5x = 75m

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Q:

If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:

A) 1:1	B) 1:2
C) 1:3	D) 1:4

Answer & Explanation Answer: A) 1:1

Explanation:

A square and a rhombus on the same base are equal in area

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Q:

If the diagonals of a rhombus are 24cm and 10cm the area and the perimeter of the rhombus are respectively.

A) 10	B) 11
C) 12	D) 13

Answer & Explanation Answer: D) 13

Explanation:

Area = $\frac{1}{2} * d i a g o n a l 1 * \frac{1}{2} d i a g o n a l 2$ = $\frac{1}{2} * 24 * 10$ sq.cm

$\frac{1}{2} * d a i g o n a l 1 = \frac{1}{2} * 24 = 12 c m$

$\frac{1}{2} * d i a g o n a l 2 = \frac{1}{2} * 10 = 5 c m$

side of a rhombus = (12)² + (5)² = 169 => AB = 13cm

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Q:

If a parallelogram with area p, a triangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then

A) P=R	B) P=A
C) P=A/2	D) P=2R

Answer & Explanation Answer: A) P=R

Explanation:

let each have base = b and height = h
then p = b*h, R = b*h and T = (1/2) * b*h
so P = R, P = 2T and T = (1/2)*R are all correct statements

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Q:

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A) 136	B) 236
C) 336	D) 436

Answer & Explanation Answer: C) 336

Explanation:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

s=1/2 x (30+14+40) = 42

Area of triangle ABC = $\sqrt{[s (s - a) (s - b) (s - c)]}$

= $\sqrt{[42 (12) (28) (2)]}$ = 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m

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Q:

The ratio of bases of two triangles is x:y and that of their areas is a:b. Then the ratio of their corresponding altitudes wll be

A) ay:bx	B) a:b
C) x:y	D) bx:ay

Answer & Explanation Answer: A) ay:bx

Explanation:

a : b =(1/2 * x * H) : (1/2 * y * h)

bxH = ayh => H/h =ay/bx

Hence H:h = ay:bx

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Q:

Find the perimeter and area of a square that has a side of length 14 feet.

A) 176	B) 186
C) 196	D) 206

Answer & Explanation Answer: C) 196

Explanation:

Perimeter of a square p=4s ,where s=length of its side

=> p=4(14)=56 feets

Area of a square A = s x s

=> A=196

The perimeter is 56 feet, and the area is 196 square feet.

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