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The following octagon is formed by removing four congruent right triangles from a rectangle. What is the total area of

the octagon?
44 cm 2
52 cm 2
10 cm 2
58 cm 2

The following octagon is formed by removing four congruent right triangles from a-example-1

1 Answer

3 votes

10cm^

To find the total area of the octagon, we need to find the area of the rectangle and subtract the areas of the four congruent right triangles that were removed.

Let's assume the length of the rectangle is L and the width is W.

The area of the rectangle is L * W.

The two smaller sides of the right triangle are congruent to the width of the rectangle, which is W. The hypotenuse of each right triangle is congruent to the length of the rectangle, which is L.

The area of a right triangle is (base * height) / 2. In this case, the base is W and the height is L.

So, the area of one right triangle is (W * L) / 2.

Since there are four congruent right triangles, the total area of the right triangles is 4 * (W * L) / 2 = 2 * (W * L).

Therefore, the total area of the octagon is (L * W) - 2 * (W * L).

The total area of the octagon = L * W - 2 * W * L.

We don't know the actual values of L and W, so we cannot calculate the exact area. However, we can simplify the expression.

The total area of the octagon = L * W - 2 * W * L = LW - 2WL = LW - 2WL = LW - 2WL = LW.

Therefore, the total area of the octagon is equal to the area of the rectangle.

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