Question

find the perimeter and area of each rectangle or square.
find the unknown side length.
solve.
7 kaya is wallpapering one wall of her room. the wall is 10 ft
long and 8 ft tall. how many square feet of wallpaper will
kaya need?
8 mias room is 12 ft long and 10 ft wide. she wants to put
a border at the top of the walls. how many feet of border does
she need?
9 a rectangular wall measures 15 ft along the floor. the area of
the wall is 180 ft². what is the height of the wall?
10 corey is tiling a rectangular bathroom that is 6 ft by 8 ft.
each tile covers 2 ft². how many tiles will he need?

Explanation:

Step1: Calculate perimeter and area for rectangle (length \(l = 5\)cm, width \(w=3\)cm)

Perimeter formula \(P = 2(l + w)\), so \(P=2(5 + 3)=16\)cm. Area formula \(A=l\times w\), so \(A = 5\times3 = 15\)cm².

Step2: Calculate perimeter and area for square (side \(s = 3\)cm)

Perimeter formula \(P = 4s\), so \(P=4\times3 = 12\)cm. Area formula \(A=s^{2}\), so \(A=3^{2}=9\)cm².

Step3: Calculate perimeter and area for rectangle (length \(l = 8\)cm, width \(w = 5\)cm)

Perimeter formula \(P = 2(l + w)\), so \(P=2(8 + 5)=26\)cm. Area formula \(A=l\times w\), so \(A=8\times5 = 40\)cm².

Step4: Find unknown side \(b\) of rectangle (\(A = 18\)cm², \(l = 6\)cm)

Using \(A=l\times b\), then \(b=\frac{A}{l}=\frac{18}{6}=3\)cm.

Step5: Find unknown side \(h\) of rectangle (\(A = 14\)cm², \(l = 7\)cm)

Using \(A=l\times h\), then \(h=\frac{A}{l}=\frac{14}{7}=2\)cm.

Step6: Find side \(s\) of square (\(A = 49\)cm²)

Using \(A=s^{2}\), then \(s=\sqrt{49}=7\)cm.

Step7: Calculate area of wall (\(l = 10\)ft, \(h = 8\)ft)

Using \(A=l\times h\), \(A=10\times8 = 80\)ft².

Step8: Calculate perimeter of room (\(l = 12\)ft, \(w = 10\)ft)

Using \(P = 2(l + w)\), \(P=2(12 + 10)=44\)ft.

Step9: Find height \(h\) of wall (\(A = 180\)ft², \(l = 15\)ft)

Using \(A=l\times h\), then \(h=\frac{A}{l}=\frac{180}{15}=12\)ft.

Step10: Calculate number of tiles

Area of bathroom \(A = 6\times8=48\)ft². Number of tiles \(n=\frac{48}{2}=24\).

Answer:

1. \(P = 16\)cm, \(A = 15\)cm²
2. \(P = 12\)cm, \(A = 9\)cm²
3. \(P = 26\)cm, \(A = 40\)cm²
4. \(b = 3\)cm
5. \(h = 2\)cm
6. \(s = 7\)cm
7. \(80\)ft²
8. \(44\)ft
9. \(12\)ft
10. \(24\) tiles