Area of Composite Shapes

Freddie and Zuri are ready to be architects for the day! They want to ensure that the area of the building isn't too big, but the floor plan is a composite shape! Let's learn all about how to find the area of composite shapes. A composite shape is a figure that consists of two or more shapes put together. To find the area of a composite shape, first, decompose, or break down, the composite shape into regular shapes, like rectangles. Then, find the area of each individual rectangle using area equals length multiplied by width. Finally, add together the area of all decomposed shapes to find the total area of the composite shape, adding the unit of measurement needed. Let's practice before we help Zuri and Freddie. First, decompose the shape. This shape can be decomposed two ways to make two regular shapes. For this shape, let's separate it here. There are now two rectangles which we can label A and B. Next, find the area of both rectangles. Starting with rectangle A, use length times width to solve for area. When shapes are decomposed, use only the measurements that cover its full length and width. Use five for length and two for width! Five times two equals ten, making the area of rectangle A ten square units. Now solve rectangle B. Use five for length and three for width. Five times three equals fifteen, so rectangle B has an area of fifteen square units. Finally, add together the area of rectangle A and rectangle B to find the area of the entire composite shape. Ten plus fifteen equals twenty-five. The composite shape has an area of twenty-five square units. Check the answer by counting all the unit squares inside the composite shape, which is twenty-five. Now we have looked at finding the area of a composite shape, let's help Zuri and Freddie calculate the area of the building using the floor plan. What is the first step? Decompose the composite shape. Let's separate it here, like this. We have a rectangle and a square, so label them A and B. What is the next step? Find the area of both shapes, starting with shape A. Remember, we can find the area multiplying length by width. What is the length and width of shape A? It is four and two. Now solve the equation. What is four times two? Eight, so the area of shape A is eight square units. Now, let's find the area of shape B. What is the length and width of shape B? It is six and six. Now solve the equation. What is six times six? Thirty-six, so the area of shape B is thirty-six square units. What is the final step? Add together the are of shape A and shape B to find the area of the composite shape. What is eight plus thirty-six? It is forty-four, so the composite shape has an area of forty-four square units. Check the answer by counting all the unit squares inside the composite shape, which is forty-four. Zuri and Freddie decide this is the perfect size, so while they construct the building, let's review! Remember, to find the area of a composite shape, first, decompose, or break down, the composite shape into regular shapes, like rectangles and use only the measurements that cover the decomposed shapes full length and width. Then, find the area of each individual shape. Finally, add together the area of all decomposed shapes, to find the total area of the composite shape. Check your work by counting all the unit squares inside the composite shape. "Phew, that sure was a lot of hard work to build." "It was, but it looks magnificent now!" "Well, I guess we should decompose this now we are finished!"