For each right triangle, draw the rectangle made by drawing sides opposite the two shorter sides in the triangle. Find the area of each rectangle.

9cm height
4cm width

How does the area of each rectangle relate to the area of either triangle inside it?

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Right side

To find the area of the rectangle made by drawing sides opposite the two shorter sides in a right triangle, you'll need to multiply the lengths of the two shorter sides of the triangle.

In this case, the height of the rectangle is given as 9 cm and the width is given as 4 cm. To calculate the area, you would multiply the height by the width:

Area of Rectangle = Height * Width

Area of Rectangle = 9 cm * 4 cm

Area of Rectangle = 36 cm²

Now, let's examine the relationship between the area of the rectangle and the area of the triangle inside it.

The triangle inside the rectangle is a right triangle. The formula to find the area of a right triangle is (1/2) * base * height, where the base and height of the triangle are the two shorter sides of the triangle.

In this case, the base and height of the triangle are 4 cm and 9 cm, respectively.

Area of Triangle = (1/2) * base * height

Area of Triangle = (1/2) * 4 cm * 9 cm

Area of Triangle = 18 cm²

Notice that the area of the rectangle (36 cm²) is twice the area of the triangle (18 cm²). This relationship will hold true for any right triangle and its associated rectangle.

So, the area of each rectangle formed by drawing sides opposite the two shorter sides in a right triangle is exactly twice the area of the triangle inside it.