krit.club logo

Measurement - Perimeter and Area of Rectangles

Grade 4IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Perimeter is the total distance around the outside edge of a 2D shape. For a rectangle, it is the sum of all four sides (l+w+l+wl + w + l + w).

Diagram of a rectangle showing sides labeled length and width to illustrate perimeter.
•

Area is the amount of surface space inside a shape, measured in square units (like cm2cm^2 or m2m^2). It is calculated by multiplying the length by the width.

A rectangle divided into a grid of unit squares to represent area.
•

A square is a special type of rectangle where all four sides are equal. Therefore, the Area = s×ss \times s and the Perimeter = 4×s4 \times s.

•

When measuring perimeter, use linear units (e.g., cmcm, mm). When measuring area, use square units (e.g., cm2cm^2, m2m^2).

📐Formulae

Perimeter of a Rectangle: P=2×(l+w)P = 2 \times (l + w) or P=(2×l)+(2×w)P = (2 \times l) + (2 \times w)

Area of a Rectangle: A=l×wA = l \times w

Perimeter of a Square: P=4×sP = 4 \times s

Area of a Square: A=s×sA = s \times s

💡Examples

Problem 1:

A rectangular rug has a length of 9m9 m and a width of 4m4 m. Find its perimeter and area.

Solution:

  1. To find the Perimeter (PP): P=2×(l+w)P = 2 \times (l + w) P=2×(9m+4m)P = 2 \times (9 m + 4 m) P=2×13m=26mP = 2 \times 13 m = 26 m

  2. To find the Area (AA): A=l×wA = l \times w A=9m×4m=36m2A = 9 m \times 4 m = 36 m^2

Explanation:

We identify the length (9m9 m) and width (4m4 m). For perimeter, we add the sides and double the sum. For area, we multiply the two dimensions together. Note the different units: mm for perimeter and m2m^2 for area.

Problem 2:

A square photo frame has a side length of 12cm12 cm. Calculate the total length of wood needed for the frame and the space the photo occupies.

Solution:

  1. The length of wood needed is the Perimeter (PP): P=4×sP = 4 \times s P=4×12cm=48cmP = 4 \times 12 cm = 48 cm

  2. The space occupied is the Area (AA): A=s×sA = s \times s A=12cm×12cm=144cm2A = 12 cm \times 12 cm = 144 cm^2

Explanation:

Since the frame is a square, all four sides are 12cm12 cm. The 'length of wood' refers to the distance around the edge (perimeter), while 'space occupied' refers to the flat surface inside (area).

Problem 3:

A rectangular garden has a length of 15m15 m and a width of 8m8 m. Find the perimeter and the area of the garden.

A rectangle labeled 15 m by 8 m.

Solution:

  1. Perimeter: P=2×(l+w)P = 2 \times (l + w) P=2×(15+8)P = 2 \times (15 + 8) P=2×23=46mP = 2 \times 23 = 46 m
  2. Area: A=l×wA = l \times w A=15×8=120m2A = 15 \times 8 = 120 m^2

Explanation:

To find the perimeter, we add the length and width and then double the result. To find the area, we multiply the length by the width.

Problem 4:

A square tile has a side length of 25cm25 cm. Calculate its area and perimeter.

A square with side labels of 25 cm.

Solution:

  1. Area: A=s×sA = s \times s A=25×25=625cm2A = 25 \times 25 = 625 cm^2
  2. Perimeter: P=4×sP = 4 \times s P=4×25=100cmP = 4 \times 25 = 100 cm

Explanation:

Since it is a square, all sides are equal. The area is the side length squared, and the perimeter is four times the side length.