Question Video: Finding the Area of Composite Figures Mathematics • 6th Grade

Determine the area of the figure.


Video Transcript

Determine the area of the given figure.

Looking at the diagram, we can see that we have a composite polygon. So, we just need to carefully identify the individual polygons it’s made up of. Firstly, we have a trapezoid. We know that the two lines which appear to be horizontal are parallel because they each form a right angle with the dotted line which appears to be vertical. We then have two congruent shapes, which are in fact parallelograms. Although, they could each be divided into a right-angled triangle and another trapezoid.

We know the formulae for calculating the areas of each of these polygons. Let’s consider the trapezoid first of all. The two parallel sides 𝑎 and 𝑏 are 16 plus 16 meters, that’s 32 meters, and 46 meters. And the perpendicular height is 14 meters. So, substituting into the formula for the area of a trapezoid gives 546.

For each of the parallelograms, and it may help here to turn your head to the side slightly, we see that they have a base of 27 meters and a perpendicular height of 14 meters. We need to be careful here. It is the perpendicular height we need, which is 14 meters, not the slant height, which is 16 meters. Remember these two parallelograms are identical or congruent. So, we can find each area, 27 multiplied by 14, and then double it to give the total contribution, which is 756.

The total area then is 546 for the area of the trapezoid plus 756 for the area of the two parallelograms, which is 1302. And the units for this area will be square meters.

Don’t worry if it sometimes takes you a little bit of time to identify the individual polygons that make up a composite polygon. It’s worth spending the time to do this and find the most efficient approach. You may find it helpful to tilt the diagram and look at it in different orientations.

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