Victor cut four congruent triangles off the corners of a rectangle to make a hexagon, as shown below.
What is the area of the shaded hexagon?
A rectangle that is 28 c-m long and 16 c-m wide has right triangles cut out from all four corners each with height and base length of 8 c-m.
The area of the shaded hexagon is 192 cm^2.
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To find the area of the shaded hexagon, we need to calculate the total area of the rectangle and subtract the areas of the four right triangles.
First, let's find the area of the rectangle. The formula for finding the area of a rectangle is length times width. In this case, the length is 28 cm and the width is 16 cm, so the area of the rectangle is 28 cm * 16 cm = 448 cm².
Now, let's calculate the area of each right triangle. The formula for finding the area of a triangle is 1/2 * base * height. In this case, the base length is 8 cm and the height is also 8 cm. So the area of each right triangle is 1/2 * 8 cm * 8 cm = 32 cm².
Since there are four right triangles, the total area of the four triangles is 4 * 32 cm² = 128 cm².
Finally, to find the area of the shaded hexagon, we subtract the total area of the four triangles from the area of the rectangle. So the area of the shaded hexagon is 448 cm² - 128 cm² = 320 cm².
Therefore, the area of the shaded hexagon is 320 cm².