9514 1404 393
Answer:
55%
Step-by-step explanation:
If the perimeter of the square is 40 cm, the length of each side is 1/4(40 cm) = 10 cm.
If we draw a diagonal through the shaded area, it divides the triangle into two parts. One has a base of 7 cm and a height of 10 cm; the other has a base of 4 cm and a height of 10 cm. The total area of those two triangles is the shaded area.
The area of a triangle is given by the formula ...
A = 1/2bh
Then the two triangles' area is ...
A = 1/2(7 cm)(10 cm) +1/2(4 cm)(10 cm) = (7 +4 cm)(5 cm) = 55 cm^2
The area of the square is the square of its side length:
A = (10 cm)^2 = 100 cm^2
Then the percentage of area that is shaded is ...
shaded fraction = (shaded area)/(total area)
shaded fraction = (55 cm^2)/(100 cm^2) × 100% = 55%
