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Geometry and Trigonometry / Area and volume Difficulty: Medium

A triangle has a base length of $56$ centimeters and a height of $112$ centimeters. What is the area, in square centimeters, of the triangle?

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Explanation

Choice C is correct. The area, $A$ , of a triangle is given by the formula $A = \frac{1}{2} b h$ , where $b$ is the base length and $h$ is the height of the triangle. It’s given that a triangle has a base length of $56$ centimeters and a height of $112$ centimeters. Substituting $56$ for $b$ and $112$ for $h$ in the formula $A = \frac{1}{2} b h$ yields $upper A equals left parenthesis one half right parenthesis left parenthesis 56 right parenthesis left parenthesis 112 right parenthesis$ , or $upper A equals 3,136$ . Therefore, the area, in square centimeters, of the triangle is $3,136$ .

Choice A is incorrect. This is the value of $56 plus 112$ , not $left parenthesis one half right parenthesis left parenthesis 56 right parenthesis left parenthesis 112 right parenthesis$ .

Choice B is incorrect. This is the value of $left parenthesis one fourth right parenthesis left parenthesis 56 right parenthesis left parenthesis 112 right parenthesis$ , not $left parenthesis one half right parenthesis left parenthesis 56 right parenthesis left parenthesis 112 right parenthesis$ .

Choice D is incorrect. This is the value of $left parenthesis 56 right parenthesis left parenthesis 112 right parenthesis$ , not $left parenthesis one half right parenthesis left parenthesis 56 right parenthesis left parenthesis 112 right parenthesis$ .