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Geometry and Trigonometry / Area and volume Difficulty: Medium

A triangle has a base length of $10$ centimeters and a corresponding height of $70$ centimeters. What is the area, in square centimeters, of the triangle?

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Explanation

Choice B is correct. The area, $A$ , of a triangle is given by $A = (\frac{1}{2}) b h$ , where $b$ is the length of a base of the triangle and $h$ is the corresponding height of the triangle. It's given that a triangle has a base length of $10$ centimeters and a corresponding height of $70$ centimeters. Substituting $10$ for $b$ and $70$ for $h$ in the formula $A = (\frac{1}{2}) b h$ yields $upper A equals left parenthesis one half right parenthesis left parenthesis 10 right parenthesis left parenthesis 70 right parenthesis$ , or $upper A equals 350$ . Therefore, the area, in square centimeters, of the triangle is $350$ .

Choice A is incorrect. This is the product of the given base and height of the triangle, not its area.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the sum of the given base and height of the triangle, not its area.