Question Video: Finding the Area of a Pentagon

Find the area of the pentagon, giving the answer to the nearest square unit.

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Video Transcript

Find the area of the pentagon, giving the answer to the nearest square unit.

In this question, we will be able to estimate the area of the pentagon by counting the squares inside the shape. We will begin by counting the complete squares inside the pentagon. There are 20 of these, so these will have an area of 20 square units. We now need to consider how we can fit the parts of squares together to estimate the area of the remainder of the shape. The top of our pentagon can be split into two triangles as shown, each of which is approximately the area of one square. This means that we can add two square units to our area.

The three sections shaded on the right and left of the pentagon are approximately equal to one and a half, or 1.5, square units. 1.5 plus 1.5 is equal to three, so we need to add three square units to our area. The same is true of the three sections in the bottom right and bottom left of the pentagon. Once again, these are approximately equal to 1.5, or one and a half, square units.

An estimate or approximation for the area of the pentagon is therefore equal to 20 plus two plus three plus three. The total area is therefore approximately equal to 28 square units.

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