Area formula

The area formula is used to find the number of square units a polygon encloses. The figure below shows some area formulas that are frequently used in the classroom or in the real-world.

Area of a square

The area of a square is the square of the length of one side. Let s be the length of one side.

A = s² = s × s

Area of a rectangle

The area of a rectangle is the product of its base and height.

Let b = base and let h = height

A = b × h = bh

For a rectangle, "length" and "width" can also be used instead of "base" and "height"

The area of a rectangle can also be the product of its length and width

A = length × width

Area of a circle

The area of a circle is the product of pi and the square of the radius of the circle.

Let r be the radius of the circle and let pi = π = 3.14

A = πr²

Please see the lesson about area of a circle to get a deeper knowledge.

Area of a triangle

The area of a triangle is half the product of the base of the triangle and its height.

Let b = base and let h = height

Area = (b × h)/2

Area of a parallelogram

The area of a parallelogram is the product of its base and height.

Let b = base and let h = height

A = b × h = bh

Please see the lesson about parallelogram to learn more.

Area of a rhombus

The area of a rhombus / area of a kite is half the product of the lengths of its diagonals.

Let d₁ be the length of the first diagonal and d₂ the length of the second diagonal.

A = (d₁ × d₂)/2

Area of a trapezoid

The area of a trapezoid is half the product of the height and the sum of the bases.

Let b₁ be the length of the first base, b₂ the length of the second base, and let h be the height of the trapezoid.

A = [h(b₁ + b₂)]/2

Please see the lesson about area of a trapezoid to learn more.

Area of an ellipse

The area of the ellipse is the product of π, the length of the semi-major axis, and the length of the semi-minor axis.

Let a be the length of the semi-major axis and b the length of the semi-minor axis.

A = πab

The semi-major axis is also called major radius and the semi-minor axis is called minor radius.

Let r₁ be the length of the semi-major axis and r₂ the length of the semi-minor axis.

The area is also equal to πr₁r₂

A couple of example showing how to use the area formula

Example #1

What is the area of a rectangular backyard whose length and breadth are 50 feet and 40 feet respectively?

Solution:

Length of the backyard = 50 ft

Breadth of the backyard = 40 ft

Area of the backyard = length × breadth

Area of the backyard = 50 ft × 40 ft

Area of the backyard = 2000 square feet = 2000 ft²

Example #2

The lengths of the adjacent sides of a parallelogram are 12 cm and 15 cm. The height corresponding to the 12-cm base is 6 cm. Find the height corresponding to the 15-cm base.

Solution:

A = b × h = 12 × 6 = 72 cm²

Since the area is still the same, we can use it to find the height corresponding to the 15 cm base.

A = b × h

Substitute 72 for A and 15 for b.

72 = 15 × h

Divide both sides of the equation by 15

72/15 = (15/15) × h

4.8 = h

The height corresponding to the 15 cm base is 4.8 cm.

Example #3

The diameter of a circle is 9. What is the area of the circle?