1999 CEMC Pascal Problems/Problem 9
Problem
In the diagram, each small square is cm by
cm. The area of the shaded region, in square centimeters is
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Solution
To find the area of the shaded region, we can subtract the unshaded region from the total area.
We can first label the lengths of the legs of the triangles. The unshaded region consists of two right triangles, as all of the angles of a square are right angles.
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The total area is a square with a side length of cm, meaning that we can find that the area is:
square cm
We then can find the area of each of the triangles using the formula for the area of a triangle, and add them together:
Adding these, we get:
square cm
Subtracting this from the total area, we get that the unshaded area is square cm.
~anabel.disher