Olympiad Test: Area, Perimeter And Volume - Class 5 MCQ

Area of triangle = 1/2 (b*h)

= 1/2 (13*5)

= 65/2

= 32.5 cm²

The perimeter of a triangle is calculated by adding up all its side lengths. Given the sides are:

• 7 metres
• 11 metres
• 13 metres

We can calculate the perimeter as follows:

• 7 + 11 = 18
• 18 + 13 = 31

Therefore, the perimeter is 31 metres.

area of parallelogram = base x height = 10 x 20 = 200 cm²

The perimeter of a parallelogram is calculated by adding all its sides. Given two pairs of equal sides:

• First pair: 14 m
• Second pair: 20 m

The calculation for the perimeter is as follows:

• 14 m + 20 m + 14 m + 20 m = 68 m

Thus, the perimeter of the parallelogram is 68 metres.

To find the area of a trapezoid, use the formula:

• Area = (Base1 + Base2) / 2 × Height

Steps to calculate:

• Identify the two parallel bases. Let's call them Base1 and Base2.
• Find the height (distance between the bases).
• Plug the values into the formula.

In this question:

• Base1 = 18 cm and Base2 = 14 cm.
• If the height is 8 cm, the calculation would be:
• (18 + 14) / 2 × 8 = 32 / 2 × 8 = 16 × 8 = 128 cm²

Therefore, correct answer- 128  cm²

The perimeter of the trapezoid can be calculated by summing the lengths of all its sides. Here’s how it breaks down:

• Length of side 1: 18 cm
• Length of side 2: 10 cm
• Length of side 3: 14 cm
• Length of side 4: 9 cm

To find the total perimeter:

Perimeter of the trapezoid = sum of all sides = 18 cm + 10 cm + 14 cm + 9 cm

This gives:

Perimeter = 51 cm

To find the area of the circle:

• Use the formula for the area of a circle: Area = πr²
• Given the radius (r) is 4 m, substitute the value into the formula:
• Area = π(4)²
• Calculate: Area = 16π
• Using π ≈ 3.14, compute the area:
• Area ≈ 16 × 3.14 = 50.24 m²

To find the perimeter of the circle:

• The formula for the perimeter (circumference) of a circle is 2πr.
• Given the radius r is 4 cm, we can substitute this value into the formula.
• Calculating the perimeter:
  • 2π × 4 = 8π
  • Using the approximate value of π (3.14):
  • 8 × 3.14 = 25.12 cm

To find the perimeter of the figure, follow these steps:

• Identify all the sides of the shape.
• Add up the lengths of all sides to get the total perimeter.
• Ensure all measurements are in the same unit, typically centimetres.
  
  Therefore, 5+6+5+8+6+8+(2π r /4) (where r = 6cm)
  = 5+6+5+8+6+8+9.42
  = 47.42cm

In this case, the calculated perimeter is 47.42 cm.

To find the length of each side of a square with an area of 64 cm²:

• The formula for the area of a square is: Area = side × side.
• Given that the area is 64 cm², we can write: side × side = 64.
• To find the length of one side, take the square root of the area: side = √64.
• Calculating this gives: side = 8 cm.

To find the perimeter of the figure made up of three squares, follow these steps:

• Each square has a side length of 5 cm.
• The area covered by the squares can affect how we calculate the perimeter.
• To determine the perimeter, we need to account for the external sides of the figure, not the internal connections.
• Considering the arrangement of the squares, the total external sides can be calculated as follows:
• Each square contributes some sides to the perimeter while others are internal.
• Count the external sides: for three squares arranged in a certain manner, typically one would find that the total length sums up to 30 cm.

The perimeter of the figure is therefore 30 cm.

To find the perimeter of the figure made up of three squares:

• Each square has a side length of 6 cm.
• There are a total of 8 boundary lines contributing to the perimeter.
• To calculate the perimeter, multiply the number of boundary lines by the side length:
• 8 lines × 6 cm = 48 cm.

first break it into a rectangle and square

rectangle of LxB=9x7
square of side=5
so area of rectangle = 9x7 =63
area of square = 5x5 = 25
so total  area = 63 +25
                      = 88

To find the length of each side of the square:

• The perimeter of a square is calculated using the formula: Perimeter = 4 × side length.
• Given that the perimeter is 20 cm, set up the equation:
• 4 × side length = 20 cm
• To find the side length, divide both sides by 4:
• side length = 20 cm / 4
• Thus, the length of each side is 5 cm.

Figures R and S each have 7 black squares, so they have the same area.

A) Area = 96m²

Breadth = 8m

Area = l*b

96 = l*8

l =12

Perimeter = 2(l+b)

= 2(12+8) = 40

B) Area = 110m²

Breadth = 10cm = 0.1m

Area = l*b

110 = l*0.1

l =1100

Perimeter = 2(l+b)

= 2(1100+0.1) = 2200.2

C) Area = 90m²

Length = 15cm = 0.15m

Area = l*b

90 = 0.15*b

b = 600m

Perimeter = 2(l+b)

= 2(0.15+600) = 1200.3

D) Area = 100m²

Length = 25cm = 0.25m

Area = l*b

100 = 0.25*b

b = 400m

Perimeter = 2(l+b)

= 2(0.25+400) = 800.5

The perimeter of the figure is 36 m. To find the length of DE, follow these steps:

• Identify all known side lengths of the figure.
• Add the lengths of the known sides.
• Subtract this sum from the total perimeter (36 m) to find the length of DE.

For example, if the total length of the other sides is 29 m, then:

• Length of DE = 36 m - 29 m = 7 m

Thus, the length of DE is 7 metres.

There are 6×4=24 squares and each square has an area of = 1cm². So, the area of rectangle = 6×4×1=24cm².

Let's take perimeter of recatngular garden=
2(20m+25m)= 90m

Cost of fencing every 5 m= Rs 27
Cost of fencing 90 m= $ 27/5 ×90
= $ 27× 18= $ 486