Olympiad Test: Mensuration - Class 6 MCQ

Perimeter of the rectangle
= sum of all sides
= length + breadth + length + breadth
= 2 x (length + breadth)
= 2(l+b)

The perimeter (P) of a square is given by the formula:

P = 4s

where s is the length of one side of the square in units. This formula indicates that the perimeter of a square is four times the length of one of its sides.

• Perimeter of an equilateral triangle: The perimeter of any polygon is the sum of the lengths of all its sides. In an equilateral triangle, all three sides are equal in length.


• Given: The side length of the equilateral triangle is 'a' units.


• Formula for perimeter: Since all sides of an equilateral triangle are equal, the perimeter P can be calculated as P = a + a + a = 3a units.


• Therefore, the correct answer is: B: 3a units.

• Definition: The total boundary length of a closed figure is called the perimeter.


• Calculation: To find the perimeter of a closed figure, you simply add up the lengths of all its sides.


• Units: Perimeter is typically measured in units such as inches, feet, meters, etc.


• Importance: Perimeter helps us understand the outer boundary of a shape and is crucial in determining the amount of fencing needed for a garden, the length of a race track, etc.


• Examples: For a square with side length 5 units, the perimeter would be 4 * 5 = 20 units. For a rectangle with lengths 6 units and 4 units, the perimeter would be 2 * (6 + 4) = 20 units.

• Definition: The amount of surface enclosed by a closed figure is called the area.


• Measurement: Area is measured in square units such as square meters (m²) or square centimeters (cm²).


• Formula: The formula to calculate the area of different shapes varies. For example, the area of a square is side * side, while the area of a circle is π * radius².


• Importance: Knowing the surface area of a closed figure is crucial in various fields such as construction, architecture, and geometry.


• Applications: Area calculation is used to determine the amount of material needed to cover a surface, calculate land area, and solve real-world problems.

2(l+b) = 170
2(50+b) = 170
50 + b = 170/2 = 85
b = 85−50 = 35m

length x  breadth = 630

length = 630/breadth

           = 630/15

length = 42 cm

Perimeter of plot = 2(l+b) = 2(30+15) = 90m

Distance between two stones = 10m

Therefore, number of stones = 90/10 = 9

We know that,

Area=l∗b

l=3.2m
b=1.5m
l×b=3.2×1.5 =4.80 sq m
to apply point - first count the no of digit after decimal in the numbers
like here one here in 3.2 and one in 1.5 so a total of 2
now apply decimal from back to 2 decimal place

Perimeter of garden= covering made by the 80 students
80 × 1.75 m = 140 m

Area of square 
= s × s 
= 3×3 = 9 sq. cm
Area of 25 squares 
= 25 × 9 
= 225 sq.cm

l = 900 m, b = 700 m
Perimeter = 2 (900 + 700) m = 2(1600) m = 3200 m
Perimeter for 3 rounds fence = 3(3200) m = 9600 m 
∴  Total amount spent 
= 9600×Rs. 8 = Rs. 76,800

1 sq. m = 10,000 sq. cm

l = 6m; b = 3m
Area of one plank = 6×3 = 18sq.m
Number of wooden planks = 5
Area of 5 wooden planks = 18×5 = 90 m²

Area of the poster = 2.5 × 2.5 sq. m
= 6.25sq.m Area of the wall 
= 10.5×8.5 sq.m
= 89.25sq.m
Area of the wall to be painted =(89.25-6.25) sq.m = 83.00 sq.m
Cost of painting = 83 × Rs. 12 = Rs. 996

10×5 = 50sq.m 
6×8 = 48 sq. m 
∴ The required area = 50 + 48 = 98 sq. m

Area of pond = 3m × 2m = 6 sq m
Area of park = 28 × 28
= 784 sq m
Area of the park excluding the pond
= 784-6
= 778 sq m

• Given: An isosceles triangle with equal sides of length p units and an unequal side of length q units.


• Perimeter of a triangle: The perimeter of a triangle is the sum of the lengths of its three sides.


• For an isosceles triangle: In an isosceles triangle, two sides are equal in length and one side is unequal.


• Perimeter of the isosceles triangle: To find the perimeter of the isosceles triangle, we add the lengths of the three sides, which are p, p, and q.

• Perimeter = p + p + q = 2p + q

• Given: Let the length of the rectangle be L and the breadth be B.


• Twice the sum of length and breadth: 2(L + B)


• Resultant of twice the sum of length and breadth: This is the perimeter of the rectangle, which is given by 2(L + B).


• Therefore, the correct answer is option B: Its perimeter.

• Perimeter of a square: The perimeter of a square is the sum of all its four sides.


• Given information: The perimeter of the square is 728 cm.


• Formula: Let's denote the side of the square as x. Therefore, the perimeter = 4x.


• Equation: 4x = 728


• Solve for x: Divide both sides by 4: x = 728 / 4 = 182

• Measure of the side: The measure of the side of the square is 182 cm.