As the area of a triangle is given by the formula (base · height)/2, triangles with the same height will have areas whose ratio is the same as the ratio of their bases:In the following … [Read more...] about Ratio of Areas of Triangles With the Same Height

# Area of Geometric Shapes

The area of a geometric shape is a property that describes how much space it takes up.

Regular geometric shapes like circles, parallelograms and triangles have simple formulas that give their area.

The area of irregular shapes can sometimes be computed by reducing it into several regular shapes.

Some common area formulas:

For triangles: Area = (h x b) /2

For rectangles: Area = h x w

Since a square is a special type of rectangle, its area is given by the same formula. But since in the square's case the width is the same as the hight, this becomes Area = a x a = a^{2}

A circle's area is given by the formula A_{circle}=π*r^{2}

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*Now that we've explained the basic concept of area in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## Area of Semicircle

A semicircle is half of a circle - a shape like this:It is formed by drawing the diameter of a circle - a straight line the runs from one point on the circle's circumference, through the … [Read more...] about Area of Semicircle

## Finding the Ratio of Triangle Areas With the Same Base

The area of a triangle is given by the formula (base · height)/2. Triangles that have the same base will have areas whose ratio is the same as the ratio of their heights:In the above drawing, … [Read more...] about Finding the Ratio of Triangle Areas With the Same Base

## Area of a Kite

Using the technique of partitioning a complex shape into simpler shapes, with known formulas for their areas, we can find a simple formula for the area of a kite- it is the product of the lengths of … [Read more...] about Area of a Kite

## Find the Area of the Shaded Region

Sometimes we are presented with a geometry problem that requires us to find the area of an irregular shape which can't easily be partitioned into simple shapes. For example, the one in the following … [Read more...] about Find the Area of the Shaded Region

## Find the Area of a Circle from 3 Points

Three points in a plane that are not all on the same line (not collinear) define a triangle, and any triangle can be circumscribed by a circle. So three point in a plane also define a circle. In this … [Read more...] about Find the Area of a Circle from 3 Points

## How to Find the Area of an Equilateral Triangle from the Radius of an Inscribed Circle

This problem is the opposite of the one where we found the area of the inscribed circle using the length of the side of the equilateral triangle. Here we will use the circle's radius to find the area … [Read more...] about How to Find the Area of an Equilateral Triangle from the Radius of an Inscribed Circle

## Area of an Irregular Shape

We've derived the basic formulas for the areas of regular shapes like triangles, rectangles, parallelograms and circles. But how do we proceed when presented with an irregular shape? We'll explore two … [Read more...] about Area of an Irregular Shape

## Area of a Rhombus with a 60° angle

If we know the length of a side of a rhombus with a 60° angle, we can find its area in a number of different ways. We will use different properties of parallelograms, diamonds or equilateral … [Read more...] about Area of a Rhombus with a 60° angle

## Area of a Triangle – Similar Triangles

The area of a triangle is given by the formula (base x height)/2. If we have similar triangles, their sides are proportional with a ratio given by a number called the scale factor. The same scale … [Read more...] about Area of a Triangle – Similar Triangles