This question was uploaded on 29/08/21 on social media accounts.
A semicircle is drawn inside a rectangle. It is inclined at a specific angle such that the edges of its diameter cut the side of the rectangle in 6, 8 units lengths. Find the area between the semicircle and the upper part of the rectangle.
Step 1:
Draw a vertical and a horizontal line passing through the center of the semicircle and touching the edges of that rectangle.
Step 2:
By Pythagoras Theorem, the Diameter of the circle is equals to the square root of the sum of squares of 6 and 8 which equals 10.
d = 10 ⇒ r = 5;
The upper part of the vertical line and the right side part of the horizontal line from the center of the circle are equal to r.
The horizontal line will divide the line with length 6 into two equal parts.
⇒ The bottom part of the vertical line from the center of the circle is equal to 3.
The vertical line will divide the line with length 8 into two equal parts.
⇒ The left side part of the horizontal line from the center of the circle is equal to 4.
Step 3:
Height of rectangle = r + 3 = 8
Breadth of rectangle = 4 + r = 9
Blue area = Area of the rectangle - Area of the triangle (with sides 6, 8, 10) - Area of the semicircle.
⇒ Blue area = 8×9 - 6×8/2 - π×5²/2
⇒ Blue area = 48 - 25π/2
Image Solution:
Puzzle related to Geometry, Circle, Rectangle, Area
