Q 1-The area of a parallelogram is 72 cm2 and its altitude is twice the corresponding base. What is the length of the base?

A - 6

B - 7

C - 8

D - 12

Answer - A

Explanation

"Let base =x cm.
Then, height =2x
=2x cm(∵ altitude is twice the base)
Area =x×2x=2x2

Area is given as 72 cm2
⇒2x2=72
⇒x2=36
⇒x=6 cm"

Q 2-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 - C

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



Area of triangle ABC ={s(s-a)(s-b)(s-c)

                                   = √ {42(12)(28)(2)}}= 168sq m

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

Q 3-The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

A - 4:25

B - 3:33

C - 2:25

D - 4:50

Answer - A

Explanation

"Let the diagonals of the squares be 2x and 5x.
 Then ratio of their areas will be

Area of square=(1/2*(2x)2*2):∗(1/2∗(5x)2*2)=4x2:25x2=4:25
"

Q 4-If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

A - 55%

B - 65%

C - 75%

D - 85%

Answer - C

Explanation

"Let original radius = R.

New radius = R/2
Original area =π R2  and new area =(π (R)2)/4 

Decrease in area =((3π* (R)2)/4)*(1/π R2)*100  = 75%
"

Q 5-One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?

A - 110

B - 120

C - 130

D - 140

Answer - B

Explanation

"Other side = [(17 x 17) - (15 x 15)] = (289 - 225) = 8m
Area = 15 x 8 =120 sq. m"

Q 6-If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.

A - 110

B - 120

C - 130

D - 140

Answer - B

Explanation

"let length = x and breadth = y then

2(x+y) = 46    x+y = 23

x²+y² = 17² = 289

now (x+y)² = 23²

x²+y²+2xy= 529

289+ 2xy = 529

 xy = 120

area = xy = 120 sq.cm
"

Q 7-A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A - 1

B - 2

C - 3

D - 4

Answer - C

Explanation

"Area of the park = (60 x 40) m2 = 2400 m2.

Area of the lawn = 2109 m2.

 Area of the crossroads = (2400 - 2109) m2 = 291 m2.

Let the width of the road be x metres. Then,

60x + 40x - x2 = 291

 x2 - 100x + 291 = 0

 (x - 97)(x - 3) = 0

 x = 3."

Q 8-Find the area of the rectangle or square with the given dimensions l = 5 inches, w=  3 inches

A - 13

B - 14

C - 15

D - 16

Answer - C

Explanation


Area= Length*Breadth

Q 9-Find the length of the altitude of an equilateral triangle of side 3√3 cm.

A - 1.5

B - 3.5

C - 2.5

D - 6.5

Answer - A

Explanation

"Let the length of the altitude be h.
Then, h = √3/3

             =1/2 x √3 x 3√3=1.5
"

Q 10-If the area of a square with side as equal to the area of a triangle with base a, then the altitude of the triangle is?

A - a

B - 2a

C - 5a

D - 3a

Answer - B

Explanation

"Area of a square with side a = a² sq unts

Area of a triangle with base a = (1/2) * a * h sq.unts

a² =1/2 *a *h

=> h = 2a

altitude of the triangle is 2a
"

Q 11-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 - C

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.
"

Q 12-If each side of a square is increased by 25%, find the percentage change in its area.

A - 56.25%

B - 36.25%

C - 16.25%

D - 12.25%

Answer - A

Explanation

"Let each side of the square be a. Then, area =a2 .
New side =.125a/100=5a/4 New area =(5a/4)2  =25a2/16 

Increase in area = (25a2/16)-a2=9a2/16
Increase% = 56.25%.
"

Q 13-The length of a rectangle is 12 cm. What is the width if the area is 72 cm ?

A - 6cm

B - 5cm

C - 3cm

D - 4cm

Answer - A

Explanation

Area= Length*Breadth

Q 14-The perimeter of a rectangle is 160 cm. The rectangle is 4 times longer than wide. What are the length and width of this rectangle?

A - l=65;b=16

B - l=16;b=64

C - l=64;b=16

D - l=16;b=48

Answer - C

Explanation

"P=2(l+b)

l=4b
"

Q 15-A wheelchair slalom event, athletes weave around cones and race to the finish line. A diagram of the rectangular course 30m length &16m bredth is shown. Find the area of the course.

A - 480

B - 560

C - 180

D - 460

Answer - A

Explanation

A = lw

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