Question

throughout this book, key problems have been selected as \checkpoints.\ each checkpoint problem is marked with an icon like the one at left. these checkpoint problems are provided so that you can check to be sure you are building skills at the expected level. when you have trouble with checkpoint problems, refer to the review materials and practice problems that are available in the \checkpoint materials\ section of your ebook. this problem is a checkpoint for area and perimeter of polygons. it will be referred to as checkpoint 1. for each figure, find the area and the perimeter. be sure to show all your work and include the correct units in your answer. a) perimeter: area: 12 cm 8 cm 8 cm 12 cm b) perimeter: area: 5 in. 4 in. 9.05 in. 11 in. c) parallelogram perimeter: area: 16 cm 10 cm 9 cm 10 cm 16 cm trapezoid perimeter: area: 25 m 20 m 24 m 44.67 m

Explanation:

Step1: Calculate perimeter of rectangle (a)

Perimeter of rectangle = 2×(length + width), so $P = 2\times(12 + 8)=2\times20 = 40$ cm

Step2: Calculate area of rectangle (a)

Area of rectangle = length×width, so $A=12\times8 = 96$ cm²

Step3: Calculate perimeter of triangle (b)

Perimeter of triangle = sum of side - lengths, so $P=5 + 9.05+11 = 25.05$ in

Step4: Calculate area of triangle (b)

Area of triangle = $\frac{1}{2}\times base\times height$, so $A=\frac{1}{2}\times11\times4 = 22$ in²

Step5: Calculate perimeter of parallelogram (c)

Perimeter of parallelogram = 2×(side1 + side2), so $P = 2\times(16 + 10)=2\times26 = 52$ cm

Step6: Calculate area of parallelogram (c)

Area of parallelogram = base×height, so $A = 16\times9=144$ cm²

Step7: Calculate perimeter of trapezoid

Perimeter of trapezoid = sum of side - lengths, so $P=25 + 24+44.67 + n$ (n is an unknown side - length, assuming it's not needed to be calculated from given info, we just sum the known sides for now) $P=25 + 24+44.67=93.67$ m

Step8: Calculate area of trapezoid

Area of trapezoid = $\frac{1}{2}\times(height)\times(sum\ of\ parallel\ sides)$, so $A=\frac{1}{2}\times20\times(25 + 44.67)=10\times69.67 = 696.7$ m²

Answer:

a) Perimeter: 40 cm, Area: 96 cm²
b) Perimeter: 25.05 in, Area: 22 in²
c) Perimeter: 52 cm, Area: 144 cm²
Trapezoid: Perimeter: 93.67 m, Area: 696.7 m²