ssc gd mensuration 2D

• What is Mensuration 2D?
• The Square (Area and Perimeter)
• The Rectangle (Area and Perimeter)
• The Triangle (Area Only)
• The Circle (Area and Circumference)

What is Mensuration 2D?

Mensuration is the part of math where we measure things like length, area, and volume. For your ssc gd mensuration exam, we focus on 2D shapes first.

• 2D means “Two Dimensional.” These are flat shapes, like a drawing on paper or the floor of a room.
• We measure two main things in 2D shapes:
  • Perimeter (P): This is the total distance around the outside edge. Think of running one lap around a field.
  • Area (A): This is the space inside the shape. Think of how much carpet you need to cover the floor.
• Learning the right mensuration ssc gd questions formula is the key to scoring high. We will practice many ssc gd mensuration questions here.

The Square (Area and Perimeter)

A square is a very simple shape. All four sides are exactly the same length.

Theory of the Square

• If one side is 5 cm, all four sides are 5 cm.
• We call the length of one side ‘$s$‘.
• To find the Perimeter, we add up all four sides.
• To find the Area, we multiply the side by itself.
• These formulas are very important for solving ssc gd mensuration questions pdf.

Formulas for the Square

4 Solved Examples

Example 1: Find the Perimeter

A square field has a side length of 10 meters. What is the perimeter?

Solution:

1. First, let’s understand what we need to find. We need the distance around the field (Perimeter).
2. Now, write down the formula for the Perimeter of a square: $P=4\times s$.
3. Put the numbers in. The side ($s$) is 10 meters. $P=4\times 10$.
4. Calculate it. $P=40$.
5. So, the answer is 40 meters.

Example 2: Find the Area

A square tile has a side length of 5 cm. What is its area?

Solution:

1. First, let’s understand what we need to find. We need the space the tile covers (Area).
2. Now, write down the formula for the Area of a square: $A=s^2$ or $A=s\times s$.
3. Put the numbers in. The side ($s$) is 5 cm. $A=5\times 5$.
4. Calculate it. $A=25$.
5. So, the answer is 25 square centimeters ($c{m}^2$). Remember, Area is always in square units.

Example 3: Find the Side given Perimeter

The perimeter of a square park is 80 meters. What is the length of one side? This is a common type of ssc gd mensuration questions.

Solution:

1. First, let’s understand what we know. We know $P=80$. We need to find $s$.
2. We know the formula is $P=4\times s$. We can change this to find $s$: $s=P÷4$.
3. Put the numbers in. $s=80÷4$.
4. Calculate it. $s=20$.
5. So, the side length is 20 meters.

Example 4: Find the Side given Area

The area of a square painting is 49 square meters. What is the length of its side? This uses the mensuration ssc gd questions formula for area.

Solution:

1. First, let’s understand what we know. We know $A=49$. We need to find $s$.
2. We know the formula is $A=s\times s$. We need to find the number that, when multiplied by itself, gives 49.
3. We look for the square root of 49. $7\times 7=49$.
4. So, the side ($s$) is 7.
5. The answer is 7 meters.

The Rectangle (Area and Perimeter)

A rectangle has four sides, but unlike a square, the sides are not all equal. It has a longer side (Length, $L$) and a shorter side (Breadth or Width, $B$).

Theory of the Rectangle

• The opposite sides are equal. If the Length is 10, the opposite side is also 10.
• The Perimeter is found by adding Length and Breadth, and then multiplying by 2 (because there are two lengths and two breadths).
• The Area is found by simply multiplying the Length and the Breadth.
• Mastering these ssc gd mensuration concepts is vital for the exam.

Formulas for the Rectangle

4 Solved Examples

Example 1: Find the Area

A rectangular swimming pool is 15 meters long and 8 meters wide. What is the area of the pool?

Solution:

1. First, let’s understand what we need to find. We need the space inside (Area).
2. Now, write down the formula: $A=L\times B$.
3. Put the numbers in. Length ($L$) = 15 m, Breadth ($B$) = 8 m. $A=15\times 8$.
4. Calculate it. $A=120$.
5. So, the answer is 120 square meters ($m^2$).

Example 2: Find the Perimeter

A rectangular garden is 20 meters long and 10 meters wide. What is the perimeter?

Solution:

1. First, let’s understand what we need to find. We need the distance around the garden (Perimeter).
2. Now, write down the mensuration ssc gd questions formula: $P=2(L+B)$.
3. Put the numbers in. $L=20$, $B=10$. $P=2(20+10)$.
4. Calculate the inside first: $20+10=30$.
5. Now multiply by 2: $P=2\times 30=60$.
6. So, the answer is 60 meters.

Example 3: Find the Length given Area

A rectangular plot has an area of 90 square meters. If the breadth is 9 meters, what is the length? This is a typical ssc gd mensuration questions pdf problem.

Solution:

1. First, let’s understand what we know. We know $A=90$ and $B=9$. We need to find $L$.
2. We know $A=L\times B$. We can change this to find $L$: $L=A÷B$.
3. Put the numbers in. $L=90÷9$.
4. Calculate it. $L=10$.
5. So, the length is 10 meters.

Example 4: Find the Breadth given Perimeter

The perimeter of a rectangular window is 40 cm. If the length is 12 cm, what is the breadth?

Solution:

1. First, let’s understand what we know. $P=40$, $L=12$. We need to find $B$.
2. We use the formula: $P=2(L+B)$.
3. Put the numbers in: $40=2(12+B)$.
4. Divide the perimeter by 2 first: $40÷2=20$. So, $20=12+B$.
5. Now, subtract 12 from 20 to find $B$: $B=20-12$.
6. Calculate it. $B=8$.
7. So, the breadth is 8 cm.

The Triangle (Area Only)

A triangle is a shape with three sides. For the ssc gd mensuration exam, we usually focus on finding its area.

Theory of the Triangle

• The Base ($b$) is the side the triangle rests on (the bottom).
• The Height ($h$) is the straight, vertical distance from the base up to the highest point (the apex).
• The Area of a triangle is exactly half the area of a rectangle that would surround it.
• This is a crucial mensuration ssc gd concept.

Formula for the Triangle

4 Solved Examples

Example 1: Find the Area

A triangle has a base of 10 cm and a height of 6 cm. What is its area?

Solution:

1. First, let’s understand what we need to find. We need the space inside (Area).
2. Now, write down the formula: $A=\frac{1}{2}\times b\times h$.
3. Put the numbers in. $b=10$, $h=6$. $A=\frac{1}{2}\times 10\times 6$.
4. Multiply the base and height first: $10\times 6=60$.
5. Now, take half of that: $A=60÷2=30$.
6. So, the answer is 30 square centimeters ($c{m}^2$).

Example 2: Find the Base given Area and Height

The area of a triangular flag is 40 square meters. If the height is 8 meters, what is the base? This requires using the ssc gd mensuration questions formula backwards.

Solution:

1. First, let’s understand what we know. $A=40$, $h=8$. We need to find $b$.
2. We use the formula: $A=\frac{1}{2}\times b\times h$.
3. Put the numbers in: $40=\frac{1}{2}\times b\times 8$.
4. First, multiply the Area by 2 (to remove the half): $40\times 2=80$.
5. Now we have: $80=b\times 8$.
6. To find $b$, divide 80 by 8: $b=80÷8$.
7. Calculate it. $b=10$.
8. So, the base is 10 meters.

Example 3: Find the Height given Area and Base

A triangle has an area of 100 square cm. If the base is 25 cm, what is the height?

Solution:

1. First, let’s understand what we know. $A=100$, $b=25$. We need to find $h$.
2. We use the formula: $A=\frac{1}{2}\times b\times h$.
3. Put the numbers in: $100=\frac{1}{2}\times 25\times h$.
4. First, multiply the Area by 2: $100\times 2=200$.
5. Now we have: $200=25\times h$.
6. To find $h$, divide 200 by 25: $h=200÷25$.
7. Calculate it. $h=8$.
8. So, the height is 8 cm.

Example 4: Area Calculation with Decimals

A small triangular piece of land has a base of 4.5 meters and a height of 2 meters. Find the area. This helps practice ssc gd mensuration questions pdf calculations.

Solution:

1. First, write down the formula: $A=\frac{1}{2}\times b\times h$.
2. Put the numbers in. $b=4.5$, $h=2$. $A=\frac{1}{2}\times 4.5\times 2$.
3. Notice that multiplying by 2 and then dividing by 2 cancels out!
4. $A=4.5$.
5. So, the area is 4.5 square meters ($m^2$).

The Circle (Area and Circumference)

A circle is a perfectly round shape. It does not have sides or corners.

Theory of the Circle

• Radius ($r$): The distance from the center point to the edge.
• Diameter ($d$): The distance across the circle, passing through the center. $d=2r$.
• Circumference (C): This is the perimeter of the circle (the distance around it).
• Pi ($\pi$): This is a special number used for all circle calculations. For mensuration ssc gd problems, we usually use $\pi =\frac{22}{7}$ or $\pi =3.14$.

Formulas for the Circle

4 Solved Examples

Example 1: Find the Circumference

A circular track has a radius of 7 meters. Find its circumference. (Use $\pi =\frac{22}{7}$).

Solution:

1. First, let’s understand what we need to find. We need the distance around the track (Circumference).
2. Now, write down the mensuration ssc gd questions formula: $C=2\pi r$.
3. Put the numbers in. $r=7$. $C=2\times \frac{22}{7}\times 7$.
4. We can cancel the 7 in the radius with the 7 in the denominator of $\pi$.
5. $C=2\times 22$.
6. Calculate it. $C=44$.
7. So, the circumference is 44 meters.

Example 2: Find the Area

A circular clock face has a radius of 14 cm. Find the area of the clock face. (Use $\pi =\frac{22}{7}$). This is a common ssc gd mensuration questions type.

Solution:

1. First, let’s understand what we need to find. We need the space the clock covers (Area).
2. Now, write down the formula: $A=\pi r^2$.
3. Put the numbers in. $r=14$. $A=\frac{22}{7}\times 14\times 14$.
4. Divide 14 by 7: $14÷7=2$.
5. Now multiply the remaining numbers: $A=22\times 2\times 14$.
6. $A=44\times 14$.
7. $A=616$.
8. So, the area is 616 square centimeters ($c{m}^2$).

Example 3: Find the Radius given Circumference

The circumference of a wheel is 88 cm. What is the radius of the wheel? (Use $\pi =\frac{22}{7}$).

Solution:

1. First, let’s understand what we know. $C=88$. We need to find $r$.
2. We use the formula: $C=2\pi r$.
3. Put the numbers in: $88=2\times \frac{22}{7}\times r$.
4. Multiply the numbers on the right side first: $2\times 22=44$. So, $88=\frac{44}{7}\times r$.
5. To find $r$, we move the fraction to the other side and flip it (multiply by $7/44$): $r=88\times \frac{7}{44}$.
6. Divide 88 by 44: $88÷44=2$.
7. Now multiply: $r=2\times 7=14$.
8. So, the radius is 14 cm.

Example 4: Find the Area given Diameter

A circular table has a diameter of 20 meters. Find its area. (Use $\pi =3.14$). This is a challenging ssc gd mensuration problem.

Solution:

1. First, let’s understand what we know. We know the Diameter ($d$) is 20 m. We need the Radius ($r$) for the area formula.
2. Find the Radius: $r=d÷2$. $r=20÷2=10$ meters.
3. Now, write down the formula: $A=\pi r^2$.
4. Put the numbers in. $\pi =3.14$, $r=10$. $A=3.14\times 10\times 10$.
5. Calculate $10\times 10=100$.
6. Multiply by 3.14. Multiplying by 100 moves the decimal two places to the right. $A=314$.
7. So, the area is 314 square meters ($m^2$).