Find the area of the figure in radical form with the radicals simplified.
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Question

Quizplus · Accepted Answer

The figure is a right triangle with legs of lengths $\sqrt{6}$ and $\sqrt{10}$, which can be seen through the Pythagorean Theorem: $(\sqrt{6})^2 + (\sqrt{10})^2 = 6+10=16=(4)^2$. Therefore, the area of the triangle is $\frac{1}{2}(\sqrt{6})(\sqrt{10}) = \sqrt{15}$. This can be simplified as $\sqrt{15}$ is not a perfect square. The only answer choice with $\sqrt{15}$ in it is $\boxed{	extbf{(C)}}$. There are two right triangles in the figure with legs of 6 and 8. This means that the hypotenuse has a length of 10 by the Pythagorean theorem. The figure is then a trapezoid with bases of length 6 and 8 and a height of 10. Using the formula for the area of a trapezoid, we get:

$$\frac{1}{2}(6+8)(10)=\frac{1}{2}(14)(10)=70$$

Therefore, the area of the figure is 70 in radical form. Simplifying 70, we get $\sqrt{490} = \sqrt{49\cdot10}=\boxed{	extbf{(C) } 11ebb63d_1bfd_7dd8_b851_29ff35dd1ccc_TB8475_11}$.

Find the Area of the Figure in Radical Form with the Radicals