Area and perimeter: word problems

key notes :

What is Perimeter?

Definition: The total length of the boundary of a 2D shape.

Units: cm, m, km, etc. (not squared).

Formulas:

• Rectangle: P=2×(L+B)
• Square: P=4×side
• Triangle: P=a+b+c
• Circle (circumference): P=2πr

What is Area?

Definition: The surface enclosed inside a 2D shape.

Units: cm², m², etc.

Formulas:

• Rectangle: A=L×B
• Square: A=side²
• Triangle: A=1/2×base×height
• Circle: A=πr²

Steps to Solve Word Problems

1. Read carefully and identify whether the question is about area or perimeter.
2. Note down given values (length, breadth, radius, base, height, etc.).
3. Choose the correct formula.
4. Substitute values into the formula.
5. Write the answer with proper units.

Solved Examples

Example 1: Rectangle

A rectangular garden is 15 m long and 10 m wide. Find its area and perimeter.

• Area = 15×10=150 m²
• Perimeter = 2×(15+10)=50 m

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Example 2: Square

A square playground has a side of 20 m. Find its area and perimeter.

• Area = 20²=400 m²
• Perimeter = 4×20=80 m

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Example 3: Triangle

A triangular park has base 12 m and height 8 m. Find its area.

• Area = 1/2×12×8=48 m²

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Example 4: Circle

A circular garden has radius 7 m. Find its area and perimeter (take π=3.14).

• Area = 3.14×72=153.86 m²
• Perimeter = 2×3.14×7=43.96 m²

Practice Word Problems

1. A rectangular room is 12 m long and 8 m wide. Find its area and perimeter.
2. A square tile has side 15 cm. Find its area. How many such tiles are needed to cover a floor of size 3 m × 3 m?
3. A triangle has base 10 cm and height 9 cm. Find its area.
4. A circular park has diameter 14 m. Find its area and perimeter.
5. The perimeter of a square is 48 cm. Find the area of the square.

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📌 Important Tip:

• Always check units. If dimensions are in different units (cm, m), convert them before solving.
• Perimeter → linear units (cm, m)
• Area → square units (cm², m²)

Learn with an example

Let’s practice!🖊️