The figure shows two squares of sides 9 and 3, respectively. Find the area of the black region.
+128474 The height of the larger (white) right triangle at the upper right = 6
And the height of the smaller (white) right triangle at the lower right = 3
And these triangles are siimilar
So the scale factor is 2:1
The legs of the smaller right triangle are (1/3) (3) = 1 and 3.....and its area = (1/2)(3)(1) = 3/2 = 1.5
The large white region has the area of (1/2) ( 9) (3 + 9) = 54
And the combined area of the squares = 9^2 + 3^2 = 90
So....the black area =
90 - 54 - 1.5 =
34.5 units^2
