SOLUTION: In the diagram below, ABCD is a square with sides 8 cm. Arcs of radius 8 cm are drawn with centres at B and D. Find the area of the shaded region, in cm^2 Diagram: https://img

Algebra ->  Surface-area -> SOLUTION: In the diagram below, ABCD is a square with sides 8 cm. Arcs of radius 8 cm are drawn with centres at B and D. Find the area of the shaded region, in cm^2 Diagram: https://img      Log On


   



Question 1188245: In the diagram below, ABCD is a square with sides 8 cm. Arcs of radius 8 cm are drawn with centres at B and D. Find the area of the shaded region, in cm^2

Diagram: https://imgur.com/gallery/YtR3qIy

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

use the diagonal AC to visualize two right triangles, each one has shaded segments of a circle

the shaded region is cut by diagonal into two equal portions
find the area of the one portion and double it
Capture11-29-2021-5-50-54-PM
so
Capture11-29-2021-5-52-28-PM


area of %281%2F2%29 of shaded region= %281%2F4%29 area of the circle minus area of the triangle
side of square a=8
%281%2F4%29 area of the circle=%281%2F4%29+%2A8%5E2%2Api
area of the triangle=%281%2F2%298%5E2
area of %281%2F2%29 shaded region=%281%2F4%29+%2A8%5E2%2Api-%281%2F2%298%5E2=18.27
double it
area of shaded region=2%2A18.27=36.54cm%5E2