Grade 7 Perimeter and Area

Interactive step-by-step solver for calculating the distance around and the space inside shapes.

Learning Mode
Practice Mode
Related Concepts

Step-by-Step Learning

Learn about perimeter and area for different shapes through these examples.

Example 1: Perimeter vs. Area

Explain the difference between perimeter and area.

Perimeter: The total distance around the boundary of a two-dimensional shape. It is a measure of length.

Think of fencing a garden or putting a border around a picture.

Imagine a rectangle with lines drawn along its edges.

Perimeter is the length of the boundary.

Area: The amount of surface covered by a two-dimensional shape. It is measured in square units.

Think of the space inside a room or the surface of a table.

Imagine a rectangle filled with small squares.

Area is the space inside.

Example 2: Perimeter of a Rectangle

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

Step 1: Identify the given values: Length (l) = 8 cm, Width (w) = 5 cm.
Step 2: Recall the formula for the perimeter of a rectangle:

Perimeter = 2 * (Length + Width)

Or, Perimeter = Length + Width + Length + Width

Step 3: Substitute the values into the formula:

Perimeter = 2 * (8 + 5)

Perimeter = 2 * (13)

Step 4: Calculate the perimeter.

Perimeter = 26

Result: The perimeter of the rectangle is 26 cm.

Example 3: Area of a Rectangle

Calculate the area of a rectangle with length 10 meters and width 6 meters.

Step 1: Identify the given values: Length (l) = 10 meters, Width (w) = 6 meters.
Step 2: Recall the formula for the area of a rectangle:

Area = Length * Width

Step 3: Substitute the values into the formula:

Area = 10 * 6

Step 4: Calculate the area.

Area = 60

Step 5: Remember the units for area are square units.

Result: The area of the rectangle is 60 square meters (m2).

Example 4: Perimeter of a Square

Calculate the perimeter of a square with a side length of 7 cm.

Step 1: Identify the given value: Side (s) = 7 cm.
Step 2: Recall the formula for the perimeter of a square. Since all four sides are equal:

Perimeter = 4 * Side

Or, Perimeter = Side + Side + Side + Side

Step 3: Substitute the value into the formula:

Perimeter = 4 * 7

Step 4: Calculate the perimeter.

Perimeter = 28

Result: The perimeter of the square is 28 cm.

Example 5: Area of a Square

Calculate the area of a square with a side length of 9 cm.

Step 1: Identify the given value: Side (s) = 9 cm.
Step 2: Recall the formula for the area of a square:

Area = Side * Side OR Area = Side2

Step 3: Substitute the value into the formula:

Area = 9 * 9

Step 4: Calculate the area.

Area = 81

Step 5: Remember the units for area are square units.

Result: The area of the square is 81 square cm (cm2).

Example 6: Area of a Triangle

Calculate the area of a triangle with a base of 10 cm and a height of 6 cm.

Step 1: Identify the given values: Base (b) = 10 cm, Height (h) = 6 cm.
Step 2: Recall the formula for the area of a triangle:

Area = (1/2) * Base * Height

Or, Area = (Base * Height) / 2

Step 3: Substitute the values into the formula:

Area = (1/2) * 10 * 6

Area = (10 * 6) / 2

Step 4: Calculate the area.

Area = 60 / 2

Area = 30

Step 5: Remember the units for area are square units.

Result: The area of the triangle is 30 square cm (cm2).

Practice Mode

Enter a problem to calculate the perimeter or area of a rectangle, square, or triangle.

Note: Enter problems using formats like "perimeter of rectangle l=10 w=5", "area of square s=7", "area of triangle b=12 h=8". Specify the shape and necessary dimensions (l=length, w=width, s=side, b=base, h=height).