Question

you have five activities planned. use the table below to determine the space needed for each activity so you can set it all up before the picnic begins.

	length	width	perimeter	area
water balloons	1 3/4 yards	5/6 yards
sponge toss	5 yards	5 2/7 yards
water tag	6 1/2 yards	4 2/5 yards
water limbo	3 1/2 yards	3 2/4 yards

Explanation:

Step1: Calculate perimeter and area for Slip N' Slide

• Perimeter formula for rectangle \(P = 2(l + w)\), where \(l=5\frac{1}{2}=\frac{11}{2}\) yards and \(w = 4\) yards.

\(P=2(\frac{11}{2}+4)=2(\frac{11 + 8}{2})=2\times\frac{19}{2}=19\) yards.

• Area formula \(A=l\times w\), \(A=\frac{11}{2}\times4 = 22\) square - yards.

Step2: Calculate perimeter and area for Water Balloons

• \(l = 1\frac{3}{4}=\frac{7}{4}\) yards, \(w=\frac{5}{6}\) yards.

\(P=2(\frac{7}{4}+\frac{5}{6})=2(\frac{21 + 10}{12})=2\times\frac{31}{12}=\frac{31}{6}=5\frac{1}{6}\) yards.

• \(A=\frac{7}{4}\times\frac{5}{6}=\frac{35}{24}=1\frac{11}{24}\) square - yards.

Step3: Calculate perimeter and area for Sponge Toss

• \(l = 5\) yards, \(w=5\frac{2}{7}=\frac{37}{7}\) yards.

\(P=2(5+\frac{37}{7})=2(\frac{35+37}{7})=2\times\frac{72}{7}=\frac{144}{7}=20\frac{4}{7}\) yards.

• \(A = 5\times\frac{37}{7}=\frac{185}{7}=26\frac{3}{7}\) square - yards.

Step4: Calculate perimeter and area for Water Tag

• \(l=6\frac{1}{2}=\frac{13}{2}\) yards, \(w = 4\frac{2}{5}=\frac{22}{5}\) yards.

\(P=2(\frac{13}{2}+\frac{22}{5})=2(\frac{65 + 44}{10})=2\times\frac{109}{10}=\frac{109}{5}=21\frac{4}{5}\) yards.

• \(A=\frac{13}{2}\times\frac{22}{5}=\frac{143}{5}=28\frac{3}{5}\) square - yards.

Step5: Calculate perimeter and area for Water Limbo

• \(l = 3\frac{1}{2}=\frac{7}{2}\) yards, \(w=3\frac{2}{4}=\frac{7}{2}\) yards.

\(P=2(\frac{7}{2}+\frac{7}{2})=14\) yards.

• \(A=\frac{7}{2}\times\frac{7}{2}=\frac{49}{4}=12\frac{1}{4}\) square - yards.

Answer:

Activity	Perimeter	Area
Water Balloons	\(5\frac{1}{6}\) yards	\(1\frac{11}{24}\) square - yards
Sponge Toss	\(20\frac{4}{7}\) yards	\(26\frac{3}{7}\) square - yards
Water Tag	\(21\frac{4}{5}\) yards	\(28\frac{3}{5}\) square - yards
Water Limbo	\(14\) yards	\(12\frac{1}{4}\) square - yards