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图1问题1(人教版新课标九年级上P114习题24.4复习巩固3)如图1,正方形的边长为a,以各边为直径在正方形内画半圆,求图中阴影部分的面积.解如图1,过正方形对角线交点O作OO1⊥AB,垂足为O1,连AO.S弓AO=S扇AO1O-S△AO1O=14π·(a2)2-12·(a2)2=πa216-a28.S阴=8S弓AO=8×(πa216-a28)=πa22-a2.图2问题2如图2,正方形的边长为a,以正方形ABCD的四个顶点为圆心,a2为半径画弧,求图中阴影部分图形的面积.解S阴=S正-4S扇EAF=S正-S圆=a2-π(a2)2=4-π4·a2.
Figure 1 Question 1 (PEP 4 new lesson plans on the ninth grade P114 exercises 24.4 review and consolidation 3) Figure 1, the side of the square is a, with each side of the diameter of the circle painted semicircle, and seek the area of the shaded area. Solution As shown in Figure 1, OO1⊥AB intersects the diagonal of the square and O1 is perpendicular to the diagonal of the square, with AO.So AO1O-S △ AO1O = 14π · (a2) 2-12 · (a2) 2 = πa216-a28.Sy = 8S bow AO = 8 × (πa216-a28) = πa22-a2 Figure 2 Problem 2 As shown in Figure 2, the side length of the square is a, with the four vertices of the square ABCD as the center, a2 To draw the arc for the radius, find the area of the shaded part of the graph. Solution S = S + -4 S-fan EAF = S + S-circle = a2 - π (a2) 2 = 4 - π4 · a2.