Mensuration is the branch of mathematics that deals with the measurement of geometric figures and their properties. It is particularly concerned with the calculation of various geometric quantities, such as area, volume, length, and surface area, related to two-dimensional and three-dimensional shapes.  Here are some formulas for the area and perimeter of different shapes: Circle: Area = πr2, Perimeter = 2πr Triangle: Area = 1⁄2 × b × h, Perimeter = a + b + c Square: Area = a, Perimeter = 4a Rectangle: Area = l × w, Perimeter = 2(l + w) Parallelogram: Area = b × h, Perimeter =... Show more

Mensuration is the branch of mathematics that deals with the measurement of geometric figures and their properties. It is particularly concerned with the calculation of various geometric quantities, such as area, volume, length, and surface area, related to two-dimensional and three-dimensional shapes. 

Here are some formulas for the area and perimeter of different shapes:
Circle: Area = πr2, Perimeter = 2πr
Triangle: Area = 1⁄2 × b × h, Perimeter = a + b + c
Square: Area = a, Perimeter = 4a
Rectangle: Area = l × w, Perimeter = 2(l + w)
Parallelogram: Area = b × h, Perimeter = 2(a+b)
Trapezoid: Perimeter = a + b + b + c, Area = 1⁄2( b + b ) x h
Ellipse: Perimeter ≈ 2π ( (a + b) / 2 ), Area = πrr
Hexagon: Perimeter = 6r, Area = (3√3/2 )r
Octagon: Perimeter = 8a, Area = ( 2 + 2√2 )a

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Math Practice Test: Mensuration - Area, Perimeter Of 2 - Dimensional Figures

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25 Questions

1. A square is inscribed in a 20-inch-diameter circle. What is the diameter of the circle?

10

2. A square has circles on its vertices touching each other. What % area of the square remains uncovered?

17222812

3. The area of a circle of radius ‘r’ is twice the area of a square with side length ‘b’. What is the value of ‘r/b’?

2 / π

4. How many tiles (each 1 ft square) are required to form a 1-ft border inside a room 24 feet by 14 feet?

72367476

5. It costs 30 paise per cm2 to carpet a room. The cost of carpeting a room 100 metre long and half as broad is

Rs. 23,000Rs. 15,000Rs. 10,000Rs. 17,000

6. A teacher in the class gave the above Q 19 – Q 22 to four students. Student dealing with which Q number brought the maximum area occupied with him? (such like questions are bonus questions – the extra time lost in solutions is recovered in answering these questions)

Q 19Q 21Q 22Q 20

7. In the above question, if a margin of 4 cm alongside is kept and punches are done on the remaining sheet, number of punches will reduce by?

144152160280

8. A circular wire which could cover an area of 5544 m2 was cut to form a square. Area of the square is how many m2 ?

337 m4173 m4327 m4356 m

9. The length of a rectangle is increased by 50%. By what percent would the width have to be decreased to maintain the same area?

33.3366.6750150

10. In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 m respectively. Find its area.

m300 m21500 m2600 m2

11. A trapezium with // sides as 40 and 56 and adjacent sides as 17 each shall have an area of _____ sq. unit

815415623795

12. An equilateral triangle has a circle of 192 π m2. Perimeter of the triangle is _____ cm

156145212144

13. From above question area of one such sector is _____
sq cm

90110120100

14. From Q. 3 above the difference between the maximum and the minimum area is nearest to _____ sq cm

5007502501000

15. Sides of a trapezium are 29 cm and 15 cm while non parallel sides are 12 and 8 cm. Its area in square cm is _____

100190130150

16. Another student drew the above circles inside a triangle. He was left with % of the area?

5102015

17. A triangle with sides 50,60,70 cm will have an area of_____ sq cm

1700150011001300

18. Diagonals of a rhombus are 24 cm and 10 cm. Its area numerically differs by how much from its perimeter?

52726862

19. Sides of a triangle are 48, 50, 14 cm. The difference between the greatest and the smallest altitude is _____ cm

34.5629.5624.5639.56

20. A rectangular sheet 48 x 36 cm shall have how many squared punches of 2 cm edge in it?

288389412432

21. A circle is in a square. Find the ratio of their areas

4:piepie:411:77: 11

22. A square is in a circle. Find the ratio of their areas

pie:44:pie7:1111:7

23. Which has the maximum area under it if each is made of 30 cm wire?

hexagonall equalpentagonoctagon

24. From above question No. 17 - height of each triangle is_____ cm

600200300400

25. The radius of a sphere is increased by 50%. The increase in the surface area of sphere is

200%100%150%125%