the perimeter of the trapezoid is 16 units, and the area is 16 square units.
To graph and connect the points F(-3,4), G(1,4), S(-2,0), and H(2,0), you can create a polygon by connecting the points in order. The shape formed is a trapezoid.
Now, calculate the distances between consecutive points to find the lengths of the sides:
1. \( FG = |1 - (-3)| = 4 \)
2. \( GS = |(-2) - 1| = 3 \)
3. \( SH = |2 - (-2)| = 4 \)
4. \( HF = |(-3) - 2| = 5 \)
The perimeter (\(P\)) is the sum of these side lengths:
\[ P = FG + GS + SH + HF = 4 + 3 + 4 + 5 = 16 \]
The area (\(A\)) of a trapezoid is given by the formula:
\[ A = \frac{1}{2}h(a + b) \]
where \(h\) is the height, and \(a\) and \(b\) are the lengths of the parallel sides. In this case, \(a = FG = 4\), \(b = SH = 4\), and \(h\) is the vertical distance between G and S, which is 4.
\[ A = \frac{1}{2}(4 + 4)(4) = \frac{1}{2}(8)(4) = 16 \]
Therefore, the perimeter of the trapezoid is 16 units, and the area is 16 square units.