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Video: Finding the Area of a Composite Figure Involving Triangles and Rectangles

Kathryn Kingham

Determine the perimeter and area of the accompanying figure.


Video Transcript

Determine the perimeter and area of the accompanying figure.

Let’s start with the perimeter. To find the perimeter, we need to add the length of all sides together. This trapezoid has four side lengths. But one of the side lengths is listed with three separate values that add up to equal it’s one long side.

So to find the perimeter, we list all the values around the outside of the figure and then add them together. When you add all the sides together, it equals 112 millimeters.

To find the area of a trapezoid, we can use the formula, area equals one-half height times the base one plus base two. We’ll call this base one and plug that value into our formula, 20 millimeters. We’ll call this value our base two. Base two is equal to 52 millimeters. You’ll find that if you add 16 plus 20 plus 16.

And the height of this trapezoid is here. The height of any trapezoid is the distance between base one and base two, but it has to be the perpendicular distance. This right angle lets us know that it’s a perpendicular distance from base one to base two, and the height of our trapezoid here is 12 millimeters. So we plug in 12 for the height and then we solve for area.

20 plus 52 equals 72. One-half times 12 equals six. Six times 72 equals 432. And because we’re dealing with area, we know that that means millimeters squared.

For this trapezoid, the perimeter: 112 millimeters. And the area: 432 millimeters squared.