11-Plus Mathematics: Perimeter and Area

Understanding Perimeter and Area

In 11-plus Mathematics, a crucial topic is the calculation of perimeter and area of various 2D shapes. Mastering these concepts is essential for success in the entrance exams.

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 together the lengths of all the sides.

Calculating Perimeter

For simple shapes:

• Rectangle: P = 2(length + width)
• Square: P = 4 × side
• Triangle: P = side1 + side2 + side3

For compound shapes, break the shape down into simpler shapes, calculate the perimeter of each, and then sum the lengths of the outer sides.

What is Area?

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

Calculating Area

For common shapes:

• Rectangle: A = length × width
• Triangle: A = 1/2 × base × height
• Parallelogram: A = base × height

For compound shapes, calculate the area of each individual shape and then add them together.

Difference Between Perimeter and Area

It is important to understand that perimeter is a measure of distance around a shape, while area measures the space within it. This distinction is crucial for solving problems correctly.

Problem-Solving with Perimeter and Area

In the 11-plus exams, you may encounter word problems that require you to apply your knowledge of perimeter and area. Here’s how to approach these problems:

1. Read the problem carefully to identify which shape(s) are involved.
2. Determine whether you need to calculate perimeter, area, or both.
3. Use the appropriate formulas and substitute the given values.
4. Check your work to ensure your calculations are correct.

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:

• Perimeter: P = 2(length + width) = 2(5 + 3) = 2 × 8 = 16 meters
• Area: A = length × width = 5 × 3 = 15 square meters

By practicing these concepts, you will enhance your skills in calculating perimeter and area, which are vital for the 11-plus Mathematics exam.