Reference : Area
Q1. A rectangle has a perimeter of 60 units. If its length is increased by 10% and width is decreased by 10%, the area remains unchanged. Find the original dimensions of the rectangle.
Length: 15, Width: 15
Length: 18, Width: 12
Length: 16, Width: 14
Length: 20, Width: 10
Q2. A farmer has a circular field with radius R. He wants to create a square garden within the circle such that the vertices of the square touch the circle. If the area of the square is 200 square units, find the radius of the circular field.
13.1 units
11.2 units
12.5 units
10.5 units
Q3. A triangular park has sides of lengths 13m, 14m, and 15m. A circular fountain is to be constructed at its center, touching all three sides. Find the area of the fountain.
12.4 sq m
10.5 sq m
11.8 sq m
9.3 sq m
Q4. A rectangular sheet of paper has length three times its width. When the sheet is folded in half parallel to its width, and then folded in half again parallel to its length, the area of the resulting rectangle is 108 sq cm. Find the dimensions of the original sheet.
60 cm × 20 cm
48 cm × 16 cm
54 cm × 18 cm
36 cm × 12 cm
Q5. In a circle of radius 10 units, two parallel chords of lengths 12 units and 16 units are drawn on the same side of the center. Find the distance between the chords.
5 units
3 units
4 units
2 units
Q6. A rectangle ABCD with dimensions 8 cm × 6 cm is given. Points P and Q are taken on sides AB and BC respectively such that AP:PB = 1:2 and BQ:QC = 2:1. Line PQ divides the rectangle into two parts. Find the difference in their areas.
12 sq cm
8 sq cm
10 sq cm
6 sq cm
Q7. A sector is cut from a circle of radius 14 cm. If the arc length of the sector is equal to its radius, find the area of the sector.
112 sq cm
77 sq cm
98 sq cm
49 sq cm
Q8. Two circles of radii 15 cm and 8 cm intersect such that the distance between their centers is 17 cm. Find the area of the region common to both circles.
82 sq cm
62 sq cm
76 sq cm
48 sq cm
Q9. A square piece of paper of side 20 cm is folded so that one corner meets the center. Find the area of the overlap.
100 sq cm
50 sq cm
75 sq cm
25 sq cm
Q10. A rectangle has a perimeter of 40 units. Find its dimensions if its area is maximum.
15 × 5
10 × 10
12 × 8
8 × 12
*Other References : *
AP & GP : Link
Average : Link
Boat & Stream : Link
Compound Interest : Link
Height & Distance : Link
LCM & HCF : Link
Logarithm : Link
Percentage : Link
Profit & Loss : Link
Ratio & Proportion : Link
Simple Interest : Link
Speed Distance : Link
Time & Work : Link
Trains Problem : Link
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