Geometry and TrigonometryVery hardTriangle area with the height inside a rectangle
Geometry and Trigonometry practice question
A rectangle is 12 units long and 9 units tall. A triangle is drawn with one side along the rectangle's bottom edge (the full 12 units) and its third vertex somewhere on the top edge. What is the area of the triangle?
Answer: 54
Wherever the third vertex sits on the top edge, the triangle's base is 12 and its height is the rectangle's height, 9. Area = (1/2)(12)(9) = 54, exactly half the rectangle.
Common wrong answers
- If you answered 21
- 21 is 12 + 9, adding the dimensions.
- If you answered 27
- 27 is a quarter of the rectangle, halving twice.
- If you answered 108
- 108 is the rectangle's full area; the triangle is half of it.
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