Video Transcript
Calculate the area of the given figure.
When we look at this figure, we see that it’s made up of a few shapes. And that means we don’t have one area formula for finding its area. We recognize the top part to be a triangle and the bottom part to be a rectangle. When we have a figure made up of two or more shapes, we call it a composite figure. And to find the area of a composite figure, you find the area of each of its parts and add them together. And that means we’ll need to find the area of this triangle and this rectangle and combine them.
We know to find the area of a triangle, you calculate one-half times the height times the base. And to calculate the area of a rectangle, you take its length and multiply it by its width. The main job here is then to correctly identify each of these values. The height of the triangle will be the perpendicular distance from its vertex to its base, and this distance would be the base. For the base, we have 10 meters on either side. And then the missing piece will be 23 meters, we see labeled from the bottom. And that means the base of this triangle will be 10 plus 10 plus 23, which is 43.
For the height, we’ve been given the distance from the vertex all the way to the base of the composite figure to be 32 meters. If this space is 32 meters, but we know that the bottom portion is 24 meters, we can find the height of the triangle by subtracting 24 from 32, which will give us eight meters, which means this triangle has a height of eight meters. We plug these values into our formula. The area will equal one-half times eight times 43, which is equal to 172. Since this is area and our units is meters, we’ll have 172 meters squared.
Finding the values for the rectangle portion is a bit more straightforward. We have a length of 23 meters and a width of 24 meters, which means the area of this rectangle will be 23 times 24, which is 552. Again, we’re dealing with meters, so 552 meters squared. To find the area of the composite shape, we then add these two values together, which gives us 724 meters squared.
