Find the area of an isosceles right triangle

Try it first. The answer and a worked explanation are right below it.

Quantitative Reasoning

Right triangle STU with a right angle at T, equal-length marks on legs ST and TU, and TU labeled 18.

In the figure, triangle $STU$ is a right triangle and $ST = TU$ . What is the area of triangle $STU$ ?

Select one answer.

36

81

324

648

162

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Answer: E ( $162$ )

The matching marks on $ST$ and $TU$ indicate that the two legs have equal lengths. Since $TU = 18$ , $ST = 18$ . The area of a right triangle is one-half the product of the lengths of its legs. Therefore, the area of triangle $STU$ is $(\frac{1}{2})(18)(18) = 162$ . The correct answer is Choice E.

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Quantitative Reasoning

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