The area of a two dimensional shape or geometric figure is the space contained within its perimeter.
Area formulas of common shapes
The exact area of many common shapes can be calculated using well-defined formulas.
The area of a circle with radius r is:
A = πr2
The area of a triangle with base, b, and height, h, is:
If the side lengths of the triangle are given, the area can be found using:
where a, b, and c are side lengths, and
The area of an equilateral triangle with side length, s, is:
The area of a square with side, s, is:
A = s2
The area of a rectangle with length, l, and width, w, is:
A = lw
The area of a parallelogram with base, b, and height, h, is:
A = bh
The area of a trapezoid with bases, b1 and b2, and height, h, is:
Kite and Rhombus
The area of a regular hexagon with side length s is:
The area of a regular pentagon with side length s is:
The area of a regular octagon with side length s is:
The area of an ellipse with semi-major axis, a, and semi-minor axis, b, is:
A = πab
Area of a composite figure
Many geometric figures are made up of two or more common figures, and their areas can be calculated using a combination of the area formulas above. These types of geometric figures are referred to as composite figures.
Find the area of the composite figure below to the nearest tenth. The figure is composed of an equilateral triangle, a rectangle, and a semi-circle (half of a circle).
Using the formula for the area of an equilateral triangle and side length 10:
The length and width of the rectangle are 10 in and 4 in respectively, so its area is
A = 10×4 = 40
The area of the semi-circle is one-half the area of a circle. The semi-circle has a radius of 5 and its area can be found by halving the area formula of a circle:
The total area of the composite figure is the sum of all its parts:
A = 86.6 + 40 + 39.3 = 122.6