Question Video: Finding the Area of a given Polygon

Video Transcript

Find the area of the polygon giving the answer to the nearest square unit.

In this question, we will try and calculate the area by counting the squares. There are six complete squares inside the polygon. Therefore, these will have an area of six square units. We can split the remainder of the polygon up into two triangles and one rectangle as shown. The rectangle at the top of the polygon is made up approximately of two half squares. As a half plus a half is equal to one, this has an area of one square unit.

The two triangles at either side of the polygon are congruent. This means they are identical. They will therefore have the same area. Each of the triangles covers an area approximately equal to one and a half square units. This means that the total area will be approximately equal to six plus one plus 1.5 plus 1.5. 1.5 plus 1.5 is equal to three, and six plus one equals seven. This means that the area of the polygon to the nearest square unit is 10 square units.