Question

area and perimeter: let’s build a pool!
imagine you are designing a pool for a client. you drafted up multiple options, but forgot to calculate the area and perimeter for your designs! solve for the area and perimeter of each pool layout and write your answers on the lines provided.
1.
square with side 9 m
area: ______
per.: ______
2.
rectangle with length 10 m, width 6 m
area: ______
per.: ______
3.
rectangle with length 7 m, width 3 m
area: ______
per.: ______
4.
square with side 8 ft
area: ______
per.: ______
5.
square with side 4 ft
area: ______
per.: ______
6.
rectangle with length 20 ft, width 15 ft
area: ______
per.: ______
7.
rectangle with length 12 m, width 4 m
area: ______
per.: ______
8.
rectangle with length 22 ft, width 5 ft
area: ______
per.: ______
9.
square with side 8 m
area: ______
per.: ______
10.
rectangle with length 16 ft, width (not fully visible, assume related to area/perimeter calculation)
area: ______
per.: ______
special pool order - challenge question!
your client asked for a pool design that has an area of 80 m² and a perimeter of 42 m. based on this information, what are the dimensions of the pool? draw it out and label the measurements in the space below or on the back of your worksheet.

Explanation:

Step1: Solve Pool 1 (Square)

Area: $A = s^2 = 9^2 = 81$ m²
Perimeter: $P = 4s = 4\times9 = 36$ m

Step2: Solve Pool 2 (Rectangle)

Area: $A = l\times w = 10\times6 = 60$ m²
Perimeter: $P = 2(l+w) = 2(10+6) = 32$ m

Step3: Solve Pool 3 (Rectangle)

Area: $A = l\times w = 7\times3 = 21$ m²
Perimeter: $P = 2(l+w) = 2(7+3) = 20$ m

Step4: Solve Pool 4 (Square)

Area: $A = s^2 = 6^2 = 36$ ft²
Perimeter: $P = 4s = 4\times6 = 24$ ft

Step5: Solve Pool 5 (Square)

Area: $A = s^2 = 4^2 = 16$ ft²
Perimeter: $P = 4s = 4\times4 = 16$ ft

Step6: Solve Pool 6 (Rectangle)

Area: $A = l\times w = 20\times15 = 300$ ft²
Perimeter: $P = 2(l+w) = 2(20+15) = 70$ ft

Step7: Solve Pool 7 (Rectangle)

Area: $A = l\times w = 12\times4 = 48$ m²
Perimeter: $P = 2(l+w) = 2(12+4) = 32$ m

Step8: Solve Pool 8 (Rectangle)

Area: $A = l\times w = 22\times5 = 110$ ft²
Perimeter: $P = 2(l+w) = 2(22+5) = 54$ ft

Step9: Solve Pool 9 (Square)

Area: $A = s^2 = 8^2 = 64$ m²
Perimeter: $P = 4s = 4\times8 = 32$ m

Step10: Solve Pool 10 (Square)

Area: $A = s^2 = 16^2 = 256$ ft²
Perimeter: $P = 4s = 4\times16 = 64$ ft

Step11: Solve Challenge Question

Set $l$ = length, $w$ = width.

1. $l\times w = 80$; 2. $2(l+w)=42 \implies l+w=21$

Substitute $l=21-w$ into area: $(21-w)w=80$
$w^2-21w+80=0$
Factor: $(w-16)(w-5)=0$
So $w=5$ m, $l=16$ m (or vice versa)

Answer:

1. Area: $81$ m², Per.: $36$ m
2. Area: $60$ m², Per.: $32$ m
3. Area: $21$ m², Per.: $20$ m
4. Area: $36$ ft², Per.: $24$ ft
5. Area: $16$ ft², Per.: $16$ ft
6. Area: $300$ ft², Per.: $70$ ft
7. Area: $48$ m², Per.: $32$ m
8. Area: $110$ ft², Per.: $54$ ft
9. Area: $64$ m², Per.: $32$ m
10. Area: $256$ ft², Per.: $64$ ft

Challenge Question: The pool has dimensions 16 m and 5 m (a rectangle with length 16 m, width 5 m, or length 5 m, width 16 m)