Mensuration Questions

Mensuration is a discipline of geometry concerned with the measurement of area, length, and volume in two-dimensional and three-dimensional forms. A plane can be used to draw the 2D shapes. Mensuration entails the use of mathematical formulas and algebraic equations to do calculations. It is also the measurement procedure based on algebraic equations and mathematical formulas.

Mensuration is a branch of mathematics concerned with the computation of 2D and 3D geometric figures. It also looks at dimensions like length, area, lateral surface area, and volume. As a result, mensuration refers to the branch of geometry concerned with determining lengths and volumes. It explains the basic equations and properties of various figures and forms and serves as a foundation for calculation. Mensuration is credited to Leonard Digges, but Archimedes is credited with its invention.

Mensuration is a mathematical field that is used to measure things. Throughout our lives, we use measurement in a variety of situations.

Let us recall the area of different shape:

• Rectangle Area = Length x Width
• Square Area = Side2
• Triangle Area = 1/2 Base x Height
• Parallelogram Area = Base x Height
• Polygons’ perimeter = sum of their sides.
• 2πr is the circumference of the circle.

Now let us discuss some of the example of Mensuration,

Example 1:Find the area of a square with a side of 10 cm.

Solution:  Area of the given square = side × side. 

Here, side = 10 cm

On Substituting the values, 10 × 10= 100.

Therefore, the area of the square = 100 square cm.

Example 2: Evaluate the surface area of a cuboid of length 2units, width 3units, and height 4units.

Solution: Given that, length of the cuboid = 2units, width of the cuboid = 3 units, height of the cuboid = 4 units.

Surface area of the given cuboid is 2 × (lw + wh + lh) square units

= 2 × (lw + wh + lh)

= 2[(2 × 3) + (3 × 4) + (4 × 5)]

= 2(5 + 12+ 20)

= 2(37)

= 74 square units.

Therefore, the surface area of the cuboid is 74square units.

Example 3: Find the area of the circle with radius 2m.

Solution: The area of a circle = π × r2; where ‘r’ is the radius of the circle and π is a constant whose value is 22/7 or 3.14.

Area of the circle = π × r2

= 3.14 × 22

Therefore, the Area of the given circle = 12.56 square cm.

Example 4: If one side of a square is 10 cm, then find  its area and perimeter?

Solution: Given,

Length of square = 10cm

Area = side2 = 42 = 10x 10= 100 cm2

Perimeter of square = 4(sides)

As we know that, sides of any square shape are always equal, 

Therefore; Perimeter = 4(10)= 40 cm

Example 5:  A given rhombus has diagonals of length 2 cm and 3 cm, respectively. Find its area.

Solution: Given, 

The rhombus has two diagonal of length let say, d1 = 2 cm, d2 = 3 cm

Area of the given rhombus = ½ d1 d2

A = ½ x 2 x 3

A= 3cm2

Example 6: The area of a box of shape of the trapezium is 200m2, the distance between their two parallel sides is 10m and one of the parallel sides is given as  15m. evaluate the other parallel side of that box.

Solution: One of the parallel sides of of that box is a = 15m, 

Now, let another parallel side be b, height h = 10m.

The given area of trapezium = 200m2

We know, by formula;

Area of the given trapezium = ½ h (a+b)

200= ½ (10) (15+b)

15+ b = (200×2)/10

b = 40– 15= 25m

Hence the length of the other parallel side of that box is 25m.

Example 7: . A rectangle with a dimension of  4cm × 2cm is folded without overlapping to make a small cylinder of height of 2 cm. evaluate the volume of the cylinder.

Solution: Given, that the Length of the paper will be the perimeter of the base of the given cylinder and the width will be its height.

Circumference of base of cylinder = 2πr = 2cm

2 x 22/7 x r = 2cm

r = 7/22cm

Volume of cylinder = πr2h = (22/7) x (7/22)2 x 2

=0.64 cm3