sat suite question viewer

Geometry and Trigonometry / Area and volume Difficulty: Medium

The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

Back question 50 of 86 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

Explanation

The correct answer is $StartFraction 15 Over 2 EndFraction$ . The area, $A$ , of a triangle is given by the formula $A = \frac{1}{2} b h$ , where $b$ is the length of the base of the triangle and $h$ is the height of the triangle. In the right triangle shown, the length of the base of the triangle is $5$ inches, and the height is $3$ inches. It follows that $b equals 5$ and $h equals 3$ . Substituting $5$ for $b$ and $3$ for $h$ in the formula $A = \frac{1}{2} b h$ yields $upper A equals one half left parenthesis 5 right parenthesis left parenthesis 3 right parenthesis$ , which is equivalent to $upper A equals one half left parenthesis 15 right parenthesis$ , or $A = \frac{15}{2}$ . Therefore, the area of the triangle, in square inches, is $StartFraction 15 Over 2 EndFraction$ . Note that 15/2 and 7.5 are examples of ways to enter a correct answer.