SAT Right triangles and trigonometry Practice Question 10 (Medium)

SAT Owl

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

An isosceles right triangle has a hypotenuse of length $12$ . What is the area of the triangle?

$72$

$18\sqrt{2}$

$36$

$144$

Show answer and explanation

Answer: C

In a $45^\circ$ - $45^\circ$ - $90^\circ$ triangle, each leg is $\frac{\text{hypotenuse}}{\sqrt{2}} = \frac{12}{\sqrt{2}} = 6\sqrt{2}$ . The area is $\frac{1}{2}(6\sqrt{2})(6\sqrt{2}) = \frac{1}{2}(72) = 36$ .

Choice A is the product of the legs, $(6\sqrt{2})^2$ , without the factor of $\frac{1}{2}$ .

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.