Chapter 17: Geometry at Work 231Or you could add more lines to the figure. Connect X and Y, draw ZW, and extend it to meet
XY at V. Find the area of 'XZY and the area of 'XWY and subtract. If XV and YV are both
3 cm, XY is 6 cm. ZW is 4 cm, and if WV is 5 cm, you can calculate the area of 'XZY as
1
2 v^6 v 9 = 27 square centimeters, and the area of 'XWY =
1
2 v^6 v 5 = 15 square centimeters.
Subtracting 27 – 15 gives you the area of the quadrilaterals as 12 square centimeters.
It’s not uncommon to be asked to find the area of part of a figure, the portion shaded in this
picture. In problems like these, it can be confusing to find the measurements you actually need.
In this target diagram, the two outer rings are marked as 1 inch wide, but there’s no convenient
formula for the area of a ring.
MATH TRAP
When you’re looking for the area of a shaded region, be careful to take the shape
apart carefully. It’s easy to include area you don’t really want or miss area you do want
if you rush to get an answer.To find the shaded area, you’re going to have to devise a way to get the area of that outer ring.
You can deal with the circle in the middle later. It’s a circle. You know what to do with that. Try
thinking about the picture as a big gray circle with a smaller white circle sitting on top.
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