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Find the area. The figure is not drawn to scale.
A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.
To find the area of the figure, we need to find the area of each triangle separately and then add them together.
First, let's find the area of the original triangle with side 6.9 cm. To do this, we can use the formula for the area of a triangle, which is 1/2 * base * height. In this case, the base is 6.9 cm and the height is unknown.
Next, we need to find the height of the original triangle. Since the figure is not drawn to scale, we can use the height of the second right triangle, which is 4 cm, as a reference.
By observing the figure, we can see that the height of the original triangle is the sum of the heights of the two right triangles formed by extending the sides of the original triangle. So, the height of the original triangle is 4 cm + 4 cm = 8 cm.
Now, we can substitute the values into the formula for the area of the original triangle:
Area of the original triangle = 1/2 * 6.9 cm * 8 cm
= 34.8 cm²
Next, let's find the area of the second right triangle. The height is given as 4 cm and the base is unknown.
By observing the figure, we can see that the base of the second right triangle is equal to the length of the side of the original triangle, which is 6.9 cm.
Now, we can substitute the values into the formula for the area of the second right triangle:
Area of the second right triangle = 1/2 * 6.9 cm * 4 cm
= 13.8 cm²
Finally, we can find the total area by adding the areas of the two triangles together:
Total area = Area of the original triangle + Area of the second right triangle
= 34.8 cm² + 13.8 cm²
= 48.6 cm²
Therefore, the area of the given figure is 48.6 cm².