All questions of Mensuration for Grade 6 Exam

To find the new perimeter of a square when its side is doubled, we need to first calculate the new side length of the square after doubling its original side length.

Given that the original side length of the square is 6 cm, we can find the new side length by multiplying the original side length by 2.

New side length = 6 cm * 2 = 12 cm

Now that we have the new side length, we can calculate the new perimeter of the square by multiplying the new side length by 4 (since a square has four equal sides).

New perimeter = 12 cm * 4 = 48 cm

Therefore, the correct answer is option A) 48 cm.

Ec

Here 's' is a variable. The formula of getting the perimeter of a square is 4× side length. You imagine that you have a square and its 1 side length is s unit, so the answer will be 4×s= 4s units.

Perimeter

B. It's Perimeter

Yes becoz as we know equilateral triangle have all equal sides so .....it is a...ot has 3 side then a+a+a=3a

The area occupied by the wooden planks can be calculated by multiplying the length and breadth of the arrangement. Given that each wooden plank measures 6 m in length and 3 m in breadth, we can determine the area occupied by five such wooden planks arranged in order as follows:

1. Calculate the area of a single wooden plank:
- Length = 6 m
- Breadth = 3 m
- Area = Length x Breadth = 6 m x 3 m = 18 sq. m

2. Determine the total area occupied by five wooden planks:
- As we have five wooden planks arranged in order, the total area would be the sum of the areas of each individual plank.
- Total area = 18 sq. m (area of a single plank) x 5 (number of planks) = 90 sq. m

Therefore, the area occupied by five wooden planks arranged in order is 90 square meters.

So, the correct answer is option B: 90 sq. m.

Explanation:
An isosceles triangle is a triangle with two equal sides. Let's call the measure of the equal sides as "p" units and the measure of the unequal side as "q" units.

Perimeter of a triangle:
The perimeter of any polygon is the sum of the lengths of all its sides. In the case of a triangle, the perimeter is the sum of the lengths of all three sides.

Calculating the perimeter of the isosceles triangle:

The isosceles triangle has two equal sides, each measuring "p" units, and one unequal side measuring "q" units.

To calculate the perimeter, we need to add up the lengths of all three sides.

Perimeter = p + p + q

Simplifying the expression, we get:

Perimeter = 2p + q

Therefore, the correct answer is option B: 2p + q units.

Understanding the Diagonal of a Square
The diagonal of a square relates to its sides through the Pythagorean theorem. For a square, if 's' is the length of a side, the relationship is given by:
Diagonal = s√2
Given Information
- Diagonal = 8√2 cm
Finding the Side Length
To find the side length, we can rearrange the diagonal formula:
s = Diagonal / √2
Substituting the given diagonal:
s = (8√2) / √2
When we simplify this:
s = 8 cm
Calculating the Perimeter
The perimeter (P) of a square is calculated using the formula:
P = 4 × s
Now, substituting the value of 's':
P = 4 × 8 cm
P = 32 cm
Conclusion
Thus, the perimeter of the square is 32 cm, making the correct answer option 'A'.

Calculation:

To find the area of the remaining part of the wall that needs to be painted, we first need to calculate the area of the square wall poster and then subtract it from the total area of the wall.

Area of the square wall poster:
Given side of the square = 2.5 m
Area of a square = side x side
Area of the square wall poster = 2.5 x 2.5 = 6.25 sq. m

Total area of the wall:
Length of the wall = 10.5 m
Width of the wall = 8.5 m
Total area of the wall = Length x Width
Total area of the wall = 10.5 x 8.5 = 89.25 sq. m

Remaining area to be painted:
Remaining area = Total area of the wall - Area of the square wall poster
Remaining area = 89.25 - 6.25 = 83 sq. m

Cost of painting the remaining area:
Cost per sq. m = Rs. 12
Total cost = Cost per sq. m x Remaining area
Total cost = 12 x 83 = Rs. 996

Therefore, the cost of painting the remaining part of the wall with pink color is Rs. 996. Hence, the correct answer is option B.

Understanding Rectangle Dimensions
To find the perimeter of a rectangle, we need to know its length and breadth. In this case:
- Length: 150 cm
- Breadth: 1 m
Unit Conversion
Before calculating the perimeter, we must ensure both dimensions are in the same unit.
- Convert the breadth from meters to centimeters:
- 1 m = 100 cm
- Therefore, the breadth is 100 cm.
Calculating the Perimeter
The formula for calculating the perimeter (P) of a rectangle is:
P = 2 * (Length + Breadth)
Now substituting the values:
- Length = 150 cm
- Breadth = 100 cm
Substituting Values
- P = 2 * (150 cm + 100 cm)
- P = 2 * (250 cm)
- P = 500 cm
Converting Perimeter to Meters
The perimeter in centimeters is 500 cm. To convert this to meters:
- 500 cm = 5 m
Conclusion
Thus, the perimeter of the rectangle is 5 m, making the correct answer option 'C'.

Solution:
Given, the area of a square is 2401 cm^2.

To find the perimeter of the square, we need to know the length of its sides.

Let's assume the length of each side of the square is 'a' cm.

Finding the length of sides:
We know that the area of a square is given by the formula: area = side^2.
So, we can write the equation as:
2401 = a^2

Taking the square root on both sides of the equation, we get:
√2401 = √(a^2)

Simplifying, we get:
49 = a

So, the length of each side of the square is 49 cm.

Finding the perimeter of the square:
The perimeter of a square is given by the formula: perimeter = 4 * side.

Substituting the value of 'a' as 49 cm, we can calculate the perimeter as:
perimeter = 4 * 49
perimeter = 196 cm

Therefore, the perimeter of the square is 196 cm.

Hence, the correct answer is option C) 196 cm.

To find the perimeter of a regular hexagon, we need to know the length of one side. In this case, the length of each side is given as 6.5 cm.

Perimeter of a Hexagon:
A regular hexagon has six equal sides. The perimeter of a regular hexagon is calculated by multiplying the length of one side by 6.

Perimeter = Length of one side × 6

Given that the length of one side is 6.5 cm, we can substitute this value into the formula to find the perimeter.

Perimeter = 6.5 cm × 6

Calculating the Perimeter:
To calculate the perimeter, we can multiply 6.5 cm by 6.

Perimeter = 6.5 cm × 6
Perimeter = 39 cm

Therefore, the perimeter of the regular hexagon with each side measuring 6.5 cm is 39 cm.

To find the width of the room, we can use the formula for the area of a rectangle:

Area = Length × Width

Given that the length of the room is 8m and the cost of flooring is Rs 85/m2, we can calculate the total cost of flooring the room:

Total cost = Cost per square meter × Area

Given that the total cost is Rs 5100, we can substitute the values into the equation:

Rs 5100 = Rs 85/m2 × Area

Now, let's solve for the area:

Area = Rs 5100 / Rs 85/m2
Area = 60 m2

To find the width of the room, we can rearrange the formula for the area of a rectangle:

Width = Area / Length

Substituting the values into the equation:

Width = 60 m2 / 8 m
Width = 7.5 m

Therefore, the width of the room is 7.5 meters.

The correct answer is option B) 7.5 m.

**Area: The Amount of Surface Enclosed by a Closed Figure**

**Introduction**
When we talk about a closed figure, we are referring to a shape that has no openings or holes in it. Examples of closed figures include circles, squares, rectangles, triangles, and many more. The amount of surface enclosed by these closed figures is called the area. It is a fundamental concept in geometry and represents the two-dimensional space within the boundaries of the shape.

**Definition of Area**
The area of a closed figure is the measure of the surface enclosed by its boundaries. It is expressed in square units, such as square centimeters (cm²), square inches (in²), or square meters (m²). The area provides information about the size of a shape, and it helps us compare and analyze different figures.

**Calculation of Area**
The method to calculate the area varies depending on the shape of the closed figure. Here are some formulas commonly used to find the area of different shapes:

1. Square: The area of a square is given by the formula A = side × side, where A represents the area and side represents the length of one side of the square.

2. Rectangle: The area of a rectangle is calculated as A = length × width, where A is the area, length is the length of the rectangle, and width is the width of the rectangle.

3. Circle: The area of a circle is determined using the formula A = πr², where A represents the area, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

4. Triangle: The area of a triangle can be found using the formula A = ½ × base × height, where A is the area, base is the length of the base of the triangle, and height is the perpendicular distance from the base to the opposite vertex.

**Importance of Area**
Understanding the concept of area is crucial in various real-life scenarios. For instance:

1. Construction: Architects and builders need to calculate the area of rooms, floors, and land to plan and estimate resources accurately.

2. Agriculture: Farmers need to determine the area of their fields to manage irrigation, fertilizers, and crop yield.

3. Art and Design: Artists and designers consider the area of different elements to create visually appealing compositions.

4. Geometry and Mathematics: Area is a fundamental concept in geometry and plays a significant role in solving problems involving shapes and figures.

In conclusion, the amount of surface enclosed by a closed figure is referred to as the area. It is a measure of the two-dimensional space within the boundaries of a shape. The calculation of area varies depending on the shape, and it is expressed in square units. Understanding the concept of area is essential in various practical applications and mathematical contexts.