Analysis:

(1) connects PB, and the area of the shaded part is equal to the sum of the areas of the square and the semicircle in the figure minus the areas of the two triangles in the blank part;

(2) If point P is the midpoint of a semicircle and the height of the triangle PAB is PG, then G is the midpoint of AB, so the length of PG is10+10 ÷ 2 =15cm, so its area is10×1. Q is the midpoint of one side of the square, so the area of the triangle PBQ is 5×5÷2= 12.5 square centimeters;

Solution: solution: the sum of the areas of a square and a semicircle;

= 100+39.25;

= 139.25 (square centimeter);

The area of the triangle PAB is: 10× 15÷2=75 (square centimeter);

The area of triangle PBQ is 5×5÷2= 12.5 (square centimeter);

The shaded area is:139.25-75-12.5 = 51.75 (square centimeter);

A: The shadow area is 5 1.75 cm2.

This problem involves the area formula of a circle.

S=πr？ (r- radius, d- diameter, π-π).

Divide the circle into several parts evenly and you can make an approximate rectangle. The width of the rectangle is equal to the radius (r) of the circle, and the length of the rectangle is half the circumference (c) of the circle. The area of a rectangle is ab, and the area of a circle is: the square of the radius (r) of the circle times π. That is, the area of a circle = radius × radius × π.