Two Rhombuses of the equal length and width of 10 inches each and height of 7 inches are drawn inside a quarter-circle of radius 18 inches as shown in the figure below.
(a) find the perimeter of each of the Rhombuses.
(b) Find the perimeter of the quarter-circle. (Use 3.14 for Pi).
(c) Find the area of each of the Rhombuses.
(d) Find the area of the quarter circle. (Pi = 3.14).
(e) Find the area of the region inside the quarter-circle but outside the two Rhombuses.
Now post your solutions and specific difficulties. I am not about to do the assignment for you. I already took the course.
To solve this problem, we will break it down into smaller parts and calculate the required lengths and areas step by step.
(a) The perimeter of a rhombus can be found by multiplying the length of one side by 4. In this case, each side of the rhombus measures 10 inches, so the perimeter of each rhombus is 10 inches × 4 = 40 inches.
(b) The perimeter of the quarter-circle consists of three parts: the curved part (arc) and two straight parts (radii). The formula to calculate the arc length is L = (theta / 360) * 2 * pi * r, where L is the arc length, theta is the central angle of the arc, pi is approximately 3.14, and r is the radius.
In this case, the radius is 18 inches, and the central angle of a quarter-circle is 90 degrees. Substituting these values into the formula, we have L = (90 / 360) * 2 * 3.14 * 18 = 14.13 inches.
The two radii are each equal to the radius of the quarter-circle, which is 18 inches. Therefore, the total perimeter of the quarter-circle is 2 * 18 inches + 14.13 inches = 50.13 inches.
(c) The area of a rhombus can be calculated using the formula A = (diagonal1 * diagonal2) / 2, where A is the area, and diagonal1 and diagonal2 are the lengths of the diagonals.
In this case, the diagonals have equal lengths of 10 inches, so the area of each rhombus is (10 inches * 10 inches) / 2 = 50 square inches.
(d) The area of a quarter-circle can be calculated using the formula A = (pi * r^2) / 4, where A is the area, pi is approximately 3.14, and r is the radius.
In this case, the radius is 18 inches, so the area of the quarter-circle is (3.14 * 18 inches * 18 inches) / 4 = 254.34 square inches.
(e) To calculate the area of the region inside the quarter-circle but outside the two rhombuses, we need to find the area of the quarter-circle and subtract the sum of the areas of the two rhombuses.
The area of the region is 254.34 square inches - 2 * 50 square inches = 154.34 square inches.
Therefore, the answers are:
(a) The perimeter of each rhombus is 40 inches.
(b) The perimeter of the quarter-circle is 50.13 inches.
(c) The area of each rhombus is 50 square inches.
(d) The area of the quarter-circle is 254.34 square inches.
(e) The area of the region inside the quarter-circle but outside the two rhombuses is 154.34 square inches.