Perimeter and Area

Learn to calculate perimeter and area of rectangles and other shapes

Perimeter and Area

Perimeter

Perimeter is the distance around a shape. Add all the side lengths.

Rectangle Perimeter

P=2l+2wP = 2l + 2w or P=2(l+w)P = 2(l + w)

where ll = length and ww = width

Square Perimeter

P=4sP = 4s

where ss = side length

Area

Area is the amount of space inside a shape (measured in square units).

Rectangle Area

A=l×wA = l \times w

Square Area

A=s2A = s^2

Triangle Area

A=12bhA = \frac{1}{2}bh

where bb = base and hh = height

Units

  • Perimeter: linear units (cm, m, in, ft)
  • Area: square units (cm², m², in², ft²)

📚 Practice Problems

1Problem 1easy

Question:

Find the perimeter of a rectangle with length 8 cm and width 5 cm.

💡 Show Solution

Solution:

Use the formula: P=2(l+w)P = 2(l + w)

P=2(8+5)P = 2(8 + 5) P=2(13)P = 2(13) P=26P = 26

Answer: 26 cm

2Problem 2medium

Question:

A rectangular garden is 12 feet long and 7 feet wide. What is its area?

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Solution:

Use the formula: A=l×wA = l \times w

A=12×7A = 12 \times 7 A=84A = 84

Answer: 84 square feet (or 84 ft²)

3Problem 3hard

Question:

A rectangle has a perimeter of 40 inches and a length of 12 inches. What is its width? Then find the area.

💡 Show Solution

Solution:

Find width: P=2(l+w)P = 2(l + w) 40=2(12+w)40 = 2(12 + w) 40=24+2w40 = 24 + 2w 16=2w16 = 2w w=8 inchesw = 8 \text{ inches}

Find area: A=l×w=12×8=96A = l \times w = 12 \times 8 = 96

Answer: Width = 8 inches; Area = 96 in²