Question

question 8 (multiple choice worth 4 points) (04 03r lc) what is the area of trapezoid defg with coordinates d (2, 3), e (5, 3), f (3, 1), and g (2, 1)? 2 square units 3 square units 4 square units 8 square units

Explanation:

Step1: Calculate the lengths of the parallel sides

The formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\vert x_2 - x_1\vert\) when \(y_1 = y_2\).
For \(DE\): \(D(2,3)\) and \(E(5,3)\), \(DE=\vert5 - 2\vert=3\)
For \(FG\): \(F(3,1)\) and \(G(2,1)\), \(FG=\vert3 - 2\vert = 1\)

Step2: Calculate the height

The height \(h\) is the vertical distance between \(y = 3\) (the \(y\)-coordinate of \(D\) and \(E\)) and \(y = 1\) (the \(y\)-coordinate of \(F\) and \(G\)). So \(h=\vert3 - 1\vert=2\)

Step3: Use the trapezoid area formula

The area formula of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height.
Substitute \(a = 3\), \(b = 1\), \(h = 2\) into the formula: \(A=\frac{(3 + 1)\times2}{2}\)

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Answer:

4 square units