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Basketball Maths

Basketball court geometry maths challenge

A child-friendly sports challenge using court geometry to practise shapes with real examples.

Quick answer

You can use basketball court geometry to learn about shapes, measurements, and space by exploring the court's design, markings, and areas.

Learning outcome

By the end of this page, you will understand how to identify and measure different shapes on a basketball court, and you will be able to solve simple problems using the court's geometry. Success signs:
  • You can name the main shapes on a basketball court
  • You can measure distances between key markings
  • You can calculate the area of parts of the court
  • You can solve simple problems using the court's layout

Why this matters

Basketball court geometry helps you understand how space is used in sports. When you know the shapes and measurements on a court, you can better understand how players move, how scoring works, and how the court is designed for fair play. This maths is also useful for real-life situations like planning a garden, designing a room, or even playing other games that use shapes and space.

How it works

Basketball courts have many different shapes and measurements. The main court is a rectangle, and it has several key markings:
  • A centre circle (a big circle in the middle)
  • Free throw lines (two lines with circles)
  • Three-point lines (curved lines that form a semicircle)
  • Key areas (the painted boxes near the basket)
Each of these shapes has specific measurements that help players know where to stand, how far to shoot, and how to score points.

Examples you can see

Let's look at some shapes on a basketball court and how to measure them: The Court Itself The basketball court is a rectangle that is 28 metres long and 15 metres wide.
  • Length: 28 metres
  • Width: 15 metres
The Centre Circle The centre circle has a radius of 1.8 metres.
  • Radius: 1.8 metres
  • Diameter: 3.6 metres
The Free Throw Circle The free throw circle has a radius of 1.25 metres.
  • Radius: 1.25 metres
  • Diameter: 2.5 metres
The Three-Point Line The three-point line is a curved line that is 6.25 metres from the basket.
  • Distance from basket: 6.25 metres
The Key Area The key area is a rectangle that is 1.25 metres wide and 5.8 metres long.
  • Width: 1.25 metres
  • Length: 5.8 metres

Try it as a mini adventure

Adventure: Court Designer Challenge You are a court designer building a new basketball court. You have to make sure all the shapes are the right size and in the right place. Step 1: Draw a rectangle that is 28 metres long and 15 metres wide to represent the court. Step 2: Draw a circle in the middle with a radius of 1.8 metres. Step 3: Draw two lines that are 1.25 metres from the basket (this is where the free throw line is). Step 4: Draw a curved line that is 6.25 metres from the basket (this is the three-point line). Step 5: Draw a rectangle that is 1.25 metres wide and 5.8 metres long for the key area. Step 6: Measure each shape and write down the measurements. Step 7: Calculate the area of the court, the centre circle, and the key area.

Common mistakes

  • Mistake: Thinking the court is a square instead of a rectangle.
    Why it happens: Not paying attention to the length and width.
    Fix: Remember that a rectangle has different length and width, while a square has equal sides.
  • Mistake: Confusing the radius and diameter of circles.
    Why it happens: Not knowing that diameter = 2 × radius.
    Fix: Remember that diameter is twice the radius, so if the radius is 1.8 metres, the diameter is 3.6 metres.
  • Mistake: Measuring the wrong part of the court.
    Why it happens: Not understanding what each marking means.
    Fix: Use a ruler or measuring tape to check the correct distance from the basket or from the edge of the court.

Parent and carer guide

You can help your child by:
  • Looking at basketball court diagrams together
  • Using a measuring tape to measure different parts of the court
  • Practising calculating areas of rectangles and circles
  • Discussing how the court's design helps players play fairly
  • Encouraging your child to draw their own court design
What to say:
  • "Can you find the circle in the middle of the court?"
  • "How far is the three-point line from the basket?"
  • "What shape is the key area?"
What not to worry about:
  • Your child might get the measurements wrong at first
  • They might mix up shapes or measurements
  • It's normal for them to need help understanding the court's layout

Practice questions

  1. What is the area of a basketball court that is 28 metres long and 15 metres wide?
  2. What is the diameter of the centre circle if its radius is 1.8 metres?
  3. How far is the free throw line from the basket if the radius of the circle is 1.25 metres?
  4. What is the area of the key area if it is 1.25 metres wide and 5.8 metres long?
  5. What is the area of the three-point line circle if its radius is 6.25 metres?
Answers:
  1. Area = length × width = 28 × 15 = 420 square metres
  2. Diameter = 2 × radius = 2 × 1.8 = 3.6 metres
  3. The free throw line is 1.25 metres from the basket
  4. Area = length × width = 1.25 × 5.8 = 7.25 square metres
  5. Area = π × radius² = 3.14 × 6.25² = 3.14 × 39.0625 = 122.72 square metres

FAQ

What is the shape of a basketball court?

A basketball court is a rectangle.

How wide is a basketball court?

A standard basketball court is 15 metres wide.

How long is a basketball court?

A standard basketball court is 28 metres long.

What is the radius of the centre circle?

The radius of the centre circle is 1.8 metres.

How far is the three-point line from the basket?

The three-point line is 6.25 metres from the basket.