What’s The Shaded Area?
Geometry: Squares and Triangles
Three squares with given areas. Find the shaded area.
Solution
We can find the area of the two right-angled triangles adjacent to the middle square by first finding their individual bases.
For the right-angled triangle on the right, the base equals
For the right-angled triangle on the left, the base equals
We will now find the areas of the two triangles.
The triangle on the right has area
The triangle on the left has area
We will now label the diagram as follows
Consider the triangle with angle a, its area equals
Now consider the triangle with angle b, its area equals
But we know that
That means the area of the shaded triangle with the angle a equals
We also know that
Therefore, the area of the shaded triangle has the same area as the unshaded triangle.
By applying similar reasoning to the right-hand side, we get the shaded area
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Happy reading,
Barry 🍩