Geometry: Finding the Area

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Area is represented by square units (units2) since it is the space found inside a 2-dimensional surface. As an illustration, area refers to the number of boxes enclosed within a shape. Let say that each box measures 1 cm. If we will count all of it, the area is equal to 30 cm² or just simply multiply the columns and rows which is 5 cm x 6 cm = 30 cm².

Area of a Rectangle

The counting of columns and rows justified the formula of Area = Length x Width. It is very easy. All we have to do is multiply the length and the width to get the Area of a rectangle.

Area of a Triangle

Logically, triangle is half of a rectangle so the formula is Area = 1/2 (Base x Height).

Area of a Parallelogram

Noticed that the concept of the formula of parallelogram (Area = Base x Height) is almost like a combination of the formula of rectangle (Area = Length x Width) and formula of triangle which is Area = 1/2 (Base x Height). The reason is when you move the triangle from the left to the right corner, it will form the shape of a rectangle.

Area of a Trapezoid

When you move the triangle from the left to the right corner, it will be a whole rectangle with a new base so the formula for a trapezoid is Area = 1/2 (Base₁ + Base₂) x Height.

Here are the illustrative examples of different unknown numbers in a trapezoid and the ways to compute them.

Illustrations and examples are all mine.

art and flair courtesy of @PegasusPhysics