11-Plus Mathematics: Perimeter and Area

Understanding Perimeter and Area

In 11-plus Mathematics, one important topic is the calculation of perimeter and area of various 2D shapes. This knowledge is essential for solving problems related to geometry and is based on the KS2 curriculum.

What is Perimeter?

The perimeter of a shape is the total distance around the outside of the shape. To calculate the perimeter, you simply add up the lengths of all the sides.

Calculating Perimeter

• Rectangles: The perimeter P can be calculated using the formula: P = 2(length + width).
• Triangles: The perimeter is the sum of all three sides: P = side1 + side2 + side3.
• Compound Shapes: For compound shapes, break the shape into simpler shapes, calculate the perimeter of each, and sum them up.

What is Area?

The area of a shape measures the amount of space inside it. Each shape has its own formula for calculating area.

Calculating Area

• Rectangles: The area A can be calculated using the formula: A = length × width.
• Triangles: The area is given by the formula: A = 1/2 × base × height.
• Parallelograms: The area can be calculated using: A = base × height.
• Compound Shapes: To find the area of compound shapes, calculate the area of each individual shape and sum them up.

Difference Between Perimeter and Area

It is crucial to understand the difference between perimeter and area:

• Perimeter measures the distance around a shape.
• Area measures the space within a shape.

Problem-Solving with Perimeter and Area

In 11-plus exams, you may encounter problems that require you to apply your knowledge of perimeter and area in real-world contexts. For example, you might be asked to calculate the amount of fencing needed for a garden or the amount of paint required to cover a wall.

Worked Example

Problem: A rectangular garden measures 5 meters in length and 3 meters in width. Calculate the perimeter and area of the garden.

Solution:

• To find the perimeter: P = 2(length + width) = 2(5 + 3) = 2 × 8 = 16 meters.
• To find the area: A = length × width = 5 × 3 = 15 square meters.

By mastering the concepts of perimeter and area, students will be well-prepared for the 11-plus examinations.