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, first, we need to find the base of the second right triangle. We can use the Pythagorean theorem to do this.
The hypotenuse of the second right triangle is the side of the first triangle with length 6.9 cm. Let's label the two legs of the second right triangle as a and b.
Using the Pythagorean theorem, we have:
a^2 + b^2 = 6.9^2
a^2 + 4^2 = 6.9^2
a^2 + 16 = 47.61
a^2 = 47.61 - 16
a^2 = 31.61
a ≈ √31.61
a ≈ 5.62 cm
Now, we can find the area of the first triangle and the second triangle separately.
Area of the first triangle = 1/2 * base * height
Area of the first triangle = 1/2 * 6.9 cm * 4 cm
Area of the first triangle = 13.8 cm^2
Area of the second triangle = 1/2 * base * height
Area of the second triangle = 1/2 * 5.62 cm * 4 cm
Area of the second triangle = 11.24 cm^2
To find the total area of the figure, we can add the areas of the two triangles:
Total area = Area of the first triangle + Area of the second triangle
Total area = 13.8 cm^2 + 11.24 cm^2
Total area ≈ 25.04 cm^2
Therefore, the area of the figure is approximately 25.04 cm^2.