Question
In 4 to 6 complete sentences. Find the area of the following trapezoid.
D=(1,3)
E=(5,3)
F=(7,1)
G=1,-1
D=(1,3)
E=(5,3)
F=(7,1)
G=1,-1
Answers
GPT-4o mini
To find the area of the trapezoid defined by the points \(D(1,3)\), \(E(5,3)\), \(F(7,1)\), and \(G(1,-1)\), we first identify the lengths of the bases and the height. The top base, \(DE\), has a length of \(5 - 1 = 4\) units, and the bottom base, \(FG\), has a length of \(7 - 1 = 6\) units. The height of the trapezoid is the vertical distance between the parallel bases, which is the difference between the \(y\)-coordinates of points \(D\) and \(G\) (or \(F\) and \(E\)). Thus, the height is \(3 - (-1) = 4\) units.
Using the formula for the area \(A\) of a trapezoid, which is \(A = \frac{1}{2} \times (b_1 + b_2) \times h\), we substitute the values we found: \(b_1 = 4\), \(b_2 = 6\), and \(h = 4\). Therefore:
\[
A = \frac{1}{2} \times (4 + 6) \times 4 = \frac{1}{2} \times 10 \times 4 = 20
\]
The area of the trapezoid is \(20\) square units.
Using the formula for the area \(A\) of a trapezoid, which is \(A = \frac{1}{2} \times (b_1 + b_2) \times h\), we substitute the values we found: \(b_1 = 4\), \(b_2 = 6\), and \(h = 4\). Therefore:
\[
A = \frac{1}{2} \times (4 + 6) \times 4 = \frac{1}{2} \times 10 \times 4 = 20
\]
The area of the trapezoid is \(20\) square units.