Question

quiz 8 - 1: perimeter & area
find the perimeter and area of each figure. show your work by writing the formulas you
need, labeling the sides, and writing what you added to find the perimeter
1.
2.
3.

Explanation:

Step1: Perimeter of parallelogram

For a parallelogram, \(P = 2(a + b)\), where \(a = 12.5\) ft and \(b = 13.5\) ft.
\(P=2(12.5 + 13.5)=2\times26 = 52\) ft

Step2: Area of parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). Here, base \(b = 12.5\) ft and height \(h=9\) ft.
\(A = 12.5\times9=112.5\) \(ft^{2}\)

Step3: Perimeter of triangle

For a triangle with sides \(a = 17\) cm, \(b = 20\) cm and \(c = 19\) cm, \(P=a + b + c\)
\(P=17+20 + 19=56\) cm

Step4: Area of triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, base \(b = 19\) cm and height \(h = 15.7\) cm
\(A=\frac{1}{2}\times19\times15.7=149.15\) \(cm^{2}\)

Step5: Perimeter of trapezoid

For a trapezoid with sides \(a = 26\) yd, \(b = 32\) yd, \(c = 50\) yd and \(d = 32\) yd, \(P=a + b + c + d\)
\(P=26+32+50 + 32=140\) yd

Step6: Area of trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)}{2}\times h\), where \(a = 26\) yd, \(b = 50\) yd and \(h = 30\) yd
\(A=\frac{(26 + 50)}{2}\times30=38\times30 = 1140\) \(yd^{2}\)

Answer:

1. \(P = 52\) ft, \(A=112.5\) \(ft^{2}\)
2. \(P = 56\) cm, \(A = 149.15\) \(cm^{2}\)
3. \(P=140\) yd, \(A = 1140\) \(yd^{2}\)