Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A cartographer is creating a map. A particular region is a trapezoid with parallel bases measuring 12 km and 18 km, and a height of 10 km. What is the area of this region?
- A180 km²
- B150 km²
- C60 km²
- D120 km²
Show answer & explanationAnswer & explanation
Correct answer: B. 150 km²
The area of a trapezoid is given by the formula A = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the parallel bases and h is the height. Given b1 = 12 km, b2 = 18 km, and h = 10 km, the area is A = (1/2) * (12 + 18) * 10 = (1/2) * 30 * 10 = 15 * 10 = 150 km².
Why the other options are wrong
- A. This is the area of a rectangle with sides 18 and 10, or (18 * 10).
- C. This would be (12 * 10) / 2, treating it like a triangle or ignoring one base.
- D. This is the average of the bases multiplied by the height, but without the (1/2) factor if calculated incorrectly, or 12*10 = 120.
Area of a Trapezoid
The measure of the two-dimensional space enclosed by a trapezoid.
- A trapezoid has one pair of parallel sides (bases).
- The height is the perpendicular distance between the bases.
- Formula: A = (1/2) * (b1 + b2) * h.
Memory trick: Average the bases, then multiply by height, and half it.