Try this beautiful Problem based on area from AMC 8 2020.
Rectangle is inscribed in a semicircle with diameter
, as shown in the figure. Let
, and let
. What is the area of
?
Area
Semi circle
Symmetry
AMC 8 2020 Problem 13
240
Try to find the diameter of the semicircle. So the diameter will be,
The diameter of the semicircle is , so
. By symmetry,
is the midpoint of AD,So,
.
Now, apply Pythagorean Theorem to find CD,
SO the area of ABCD will be=
Try this beautiful Problem based on area from AMC 8 2020.
Rectangle is inscribed in a semicircle with diameter
, as shown in the figure. Let
, and let
. What is the area of
?
Area
Semi circle
Symmetry
AMC 8 2020 Problem 13
240
Try to find the diameter of the semicircle. So the diameter will be,
The diameter of the semicircle is , so
. By symmetry,
is the midpoint of AD,So,
.
Now, apply Pythagorean Theorem to find CD,
SO the area of ABCD will be=