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The figure above appeared in a problem on an SAT exam. All of the triangles are congruent, the area of the shaded region is 84, and the area of square ABCD is 100.
1. What is the area of one of the triangles?
2. What is the total area of the entire figure?
Four square units.
The total area of the square ABCD is 100 and the shaded area is 84. So the unshaded area, the triangles, would have an area of 100 - 84 = 16 square units. Since there are four congruent triangles, the area of each triangle is 16/4 = 4 square units.
116 square units.
The total area of the entire figure is the area of square ABCD and the triangles that are outside the square. Since each triangle is 4 sq. units, the four triangle would make 16 sq. units. Hence, the total area of the figure is 100 + 16 = 116 square units.