Answer:
a). 722 cm²
b). 412.11 cm²
Step-by-step explanation:
ABC is a quarter circle with radius CE,
Area of a quarter circle = [tex]\frac{1}{4}\pi r^{2}[/tex]
Since CDEF is a square, diagonals CE and FD will be equal.
CE ≅ FD ≅ 38cm
(a). Measure of a side of the square CDEF = [tex]\sqrt{\frac{1}{2} (\text {Diagonal})^2}[/tex]
Side = [tex]\sqrt{\frac{(38)^2}{2} }[/tex]
= 26.87
Area of the square CDEF = (Side)²
= (26.87)²
= 722 cm²
b). Area of the shaded part = Area of the quarter circle - Area of the square
Area of the quarter circle = [tex]\frac{1}{4}\pi (38)^{2}[/tex]
= 1134.11495 cm²
Area of the shaded area = 1134.11495 - 722
= 412.11495 cm²
≈ 412.11 cm²
