A quarter-circle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. The area of the figure is
33.4 square centimeters.
What is the length of the longer side of the rectangle?
Use 3.14 for tt.
Enter your answer as decimal in the box.
The area of the figure is made up of the area of the rectangle and the quarter-circle.
The area of the rectangle can be calculated as length times width = 4xL (let the longer side be L cm).
The area of the quarter-circle is (1/4)πr^2, where r is the radius of the quarter-circle and we know that the radius of the quarter circle is 4 cm (half of the short side of the rectangle).
So, we have the total area as:
4L + (1/4)π(4)^2 = 33.4
4L + 4π = 33.4
4L = 33.4 - 4π
L = (33.4 - 4π)/4
L = (33.4 - 4*3.14)/4
L = (33.4 - 12.56)/4
L = 20.84/4
L = 5.21
Therefore, the length of the longer side of the rectangle is 5.21 cm.