Learn the area formula in maths (2024)

Area in maths: A measure of the space inside a shape. Learn the area formula for various shapes and real-world applications.

• Area is how we measure the space inside of a shape. Finding the area helps us understand the size of a bedroom or football field.
• Different shapes have different area formulas.
• There are many examples of calculating area in everyday life, like buying the right amount of paint or setting up a garden.

• Key takeaways
• Area definition
• Practice questions
• FAQs

What is area? Area in maths is about counting squares. When we define area, it means how many square units fit inside a shape or figure. If you picture a square 3O units long on each side, the area is 9 square units. This is because 9 squares, each 1 unit by 1 unit, can fit inside.

The concept of works the same way for all shapes, not just squares. From circles to triangles and more complex figures, the idea is to calculate how many square units fill up that shape.

This area definition helps us understand and describe the space around us!

Think about a farmer with a rectangular field. The length of his field is 200 feet, and the width is 100 feet. The farmer needs to know the total space of his field to buy the correct amount of seeds. He multiplies the length by the width and finds out his field is 20,000 square feet.

In a different scenario, consider an architect who is designing a room. She has a perfect square room, with each side being 12 feet. She calculates the area to ensure the furniture will fit and leave enough space to move around.

By multiplying the length and the width, she determines the room is 144 square feet. From farming to house design, the concept of area is essential.

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The formula to calculate area depends on the shape in question. For basic shapes such as a square or a rectangle, the area is the product of the length and the width.

However, their area formula becomes more complicated as the shapes become complex. Let’s take a look at a variety of area formulas by shape:

• Square or rectangle: In a square or rectangle, the formula for area is simply length times width (A = l x w). This basic formula is one of the most used in area calculation. If you have a square room that measures 10 feet on each side, the area of the room would be 10 feet (length) times 10 feet (width), which equals 100 square feet. For a rectangular space, you use the length and width of the rectangle similarly.
• Circle: The formula to calculate the area of a circle is pi times the radius squared (A = πr^2). Here, the radius is the distance from the circle’s centre to its edge, and pi is a mathematical constant approximately equal to 3.14159.
• Triangle: For a triangle, the area formula is one-half the base times the height (A = ½ x b x h). This formula is used when you know the base and the height of the triangle.
• Parallelogram: The area of a parallelogram is calculated by multiplying the base by the height (A = b x h).
• Trapezium: When dealing with a trapezium, the area formula is the average of the lengths of the bases (the parallel sides) times the height (A = ½ (a + b)h)).

Volume measures the quantity of three-dimensional space an object inhabits. It’s like filling a box with small cubes and calculating how many fit inside. This measure considers not just the surface, as area does, but the entirety of the space within the object’s boundaries.

So while area and volume are related, they offer distinct ways to understand and interact with space. If you think of area as the carpet on your living room floor, volume would be the space your living room occupies, from floor to ceiling!

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