# Area Formulas to Know for the CAT

What area formulas do you need to know for the CAT? After reading this article, you’ll know the basics of geometric area computations, including the most common formulas that show up on the test.

A “tangram” consisting of triangles and other shapes.

## Area Formulas for the CAT

You will need to know the area formulas for each of the following basic shapes.

• Triangles
• Rectangles and Parallelograms
• Circles

Moreover, you should know how to break down a more complicated shape into basic shapes to find its total area.

### Triangles

The area of a triangle is: A = (1/2)bh, where b is the length of the base, and h is the height (length of the altitude).

Often you’ll have to find a suitable altitude in a triangle first.

Alternatively, if you know the lengths of each of the sides, you could use Heron’s Formula for area.

The quantity “s” is called the semiperimeter of the triangle.

By the way, you can check out Triangle Properties to Know for the CAT for more about triangles!

### Rectangles and Parallelograms

The basic rule for both rectangles and parallelograms is that Area equals Base times Height. That is,

A = bh

Rectangle with base b and height h

A parallelogram with base b and height h. Its area is the same as that of a rectangle with the same dimensions.

### Circles

The area of a circle of radius r is: A = πr2. For most purposes, you can approximate π ≈ 3.14 (or, even better, 3.14159). Remember, if the problem gives you a diameter for a circle, then its radius is half the diameter length.

### Areas of More Complicated Shapes

Other shapes may be broken down into rectangles and triangles.

For example, a trapezoid consists of a rectangle together with a triangle on either side.

But if you want to memorize another formula, you can use A = (h/2)(a + b), where h is the height, and the top and bottom bases have length a and b, respectively.

The area of a trapezoid with height h and base lengths a and b is equal to (h/2)(a + b)

A regular polygon has all sides and angles equal. You can break up a regular polygon into n congruent isosceles triangles, where n is the number of sides. Then if you can find the area of one such triangle, simply multiply that result by n to obtain the area of the whole polygon.

The area of this pentagon is 5 times the area of one central triangle.

On the other hand, if you’re good at memorizing formulas, then here’s one for the regular polygon of n sides with side length s:

## Summary

Let’s review!

• Triangles: A = (1/2)bh (or use Heron’s formula)
• Rectangles: A = bh
• Parallelograms: A = bh
• Circles: A = πr2
• Break up complicated shapes into simpler pieces to find area, or use a formula specific to that shape (if such a formula exists)

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