A composite of two rectangles. The top rectangle is a smaller rectangle and is centered on the top width of the bottom larger rectangle. The top rectangle has a label of 4 meters on the top side, and 3 meters on the left side. The top two angles of the top rectangle have right angle marks. The bottom rectangle has a label of 8 meters on the bottom side. The distance between the right side of the top rectangle to the right side of the bottom rectangle is 2 meters. All 4 angles of the bottom rectangle have right angle marks.
The area of the composite figure is 52 square meters. What is the
height of the bottom rectangle?
To find the height of the bottom rectangle, we first need to find the area of the top rectangle. The area of a rectangle is given by the formula: Area = length x width.
For the top rectangle:
Length = 4 meters
Width = 3 meters
Area of top rectangle = 4 x 3 = 12 square meters.
Now, we can find the area of the bottom rectangle. Since the total area of the composite figure is 52 square meters and the area of the top rectangle is 12 square meters, the area of the bottom rectangle is:
Area of bottom rectangle = Total area - Area of top rectangle
Area of bottom rectangle = 52 - 12 = 40 square meters.
The height of the bottom rectangle is the side opposite the 8-meter side. To find the height, we can divide the area by the length:
Height = Area / Length
Height = 40 / 8 = 5 meters.
Therefore, the height of the bottom rectangle is 5 meters.