Learn about Areas of Complex Figures Area of complex figures: So in this problem we need to find the area of this figure. So this figure that is represented is a complex figure. A complex figure is a shape made up of two or more shapes. So it’s a shape that is made up of two or more shapes. So when you have a complex figure, you can split the figure into smaller familiar parts. So let’s look at this given figure. We can divide it into similar parts; we can divide it into a rectangle and a square. So by dividing it right along here, we have our rectangle and then we have a square. All right, now to find the area, the formula that we use is the area equals the area of the rectangle plus the area of the square. So we know to find the area of a rectangle, you take the length times the width. So in this problem here, the width is 12 and our length is 15. So for the area of the rectangle, our length is 15 times our width which is 12. So 15 x 12 is 180 ft.2. So keep in mind that the unit is ft.2 because we have feet times feet, and when you have feet time feet, you get feet2 so keep that in mind. Now the area of a square is S2 okay so the area of the square is S2 where S is the side of the square. So S equals the side of the square. Okay so, here’s the side of the square 9 feet, okay so S = 9 feet in this problem. So to find the area of the square, you’re going to take the side squared and when you square something, you’re multiplying it by itself so S = 9 feet, so you’re going to take 9 x 9, and 9 x 9 is 81 and that would be feet squared because remember we you have feet times feet, you get feet2 so it’s 81 ft.2. Now, to find the area of this complex figure we’re going to take the area of the rectangle and add it to the area of the square okay, so since the area of the complex figure, the area of the rectangle— and I’m just going to rewrite this, Area of the rectangle plus the area of the square. So the area of the rectangle is 180 ft.2 plus the area of the square which is 81 ft.2 and then we get, if we add these up, we get 261 ft.2. So the area of this figure is 261 ft.2 Things to remember, and keep in mind is that a complex figure is a shape made up of two or more shapes, so one way to calculate the area of a complex figure is to think of it in simpler parts. So you split the figure up into simpler parts and then you add these two parts, add the areas of the simpler parts to find the area of the complex figure. So remember that the area of a rectangle, to find the area of a rectangle, you use the length times the width. The area of the square is the side times the side or S2. And the area is measured in feet or in square units. So remember that the area is measure in square units.