Surface area of cuboids worksheet with open and closed shapes and measurement values.

Here are the step-by-step solutions for finding the surface area of each cuboid.

Important Rule to Remember:
* Closed Cuboid: Has 6 faces (Top, Bottom, Front, Back, Left, Right).
* Formula: $2 \times (\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height})$
* Open Cuboid: Usually means the top is missing, so it has only 5 faces.
* Formula: $(\text{length} \times \text{width}) + 2 \times (\text{length} \times \text{height}) + 2 \times (\text{width} \times \text{height})$
*(Note: The "length x width" part is just the bottom base).*

---

1) Closed Cuboid

* Dimensions: Length = $9 \frac{1}{2}$ in, Width = $3$ in, Height = $4 \frac{1}{2}$ in.
* Let's use decimals to make it easier: $L = 9.5$, $W = 3$, $H = 4.5$.

Step 1: Find the area of the three pairs of faces.
* Top and Bottom: $9.5 \times 3 = 28.5$ sq in.
* Front and Back: $9.5 \times 4.5 = 42.75$ sq in.
* Left and Right sides: $3 \times 4.5 = 13.5$ sq in.

Step 2: Add them up and multiply by 2 (since there are two of each).
* Sum: $28.5 + 42.75 + 13.5 = 84.75$
* Total Surface Area: $84.75 \times 2 = 169.5$

Area: $169.5 \text{ in}^2$ (or $169 \frac{1}{2} \text{ in}^2$)

---

2) Closed Cuboid

* Dimensions: Length = $18$ cm, Width = $11$ cm, Height = $7$ cm.

Step 1: Find the area of the three pairs of faces.
* Top and Bottom: $18 \times 11 = 198$ sq cm.
* Front and Back: $18 \times 7 = 126$ sq cm.
* Left and Right sides: $11 \times 7 = 77$ sq cm.

Step 2: Add them up and multiply by 2.
* Sum: $198 + 126 + 77 = 401$
* Total Surface Area: $401 \times 2 = 802$

Area: $802 \text{ cm}^2$

---

3) Open Cuboid

* Dimensions: Length = $2.8$ m, Width = $0.5$ m, Height = $1.7$ m.
* Since it is open, we calculate the bottom base + the 4 vertical walls. We do not include the top.

Step 1: Calculate the Bottom Base.
* Area = $\text{Length} \times \text{Width} = 2.8 \times 0.5 = 1.4 \text{ m}^2$

Step 2: Calculate the 4 Walls.
* Front and Back walls ($\text{Length} \times \text{Height}$): $2.8 \times 1.7 = 4.76$. There are two, so $4.76 \times 2 = 9.52 \text{ m}^2$.
* Side walls ($\text{Width} \times \text{Height}$): $0.5 \times 1.7 = 0.85$. There are two, so $0.85 \times 2 = 1.7 \text{ m}^2$.

Step 3: Add them all together.
* Total = $1.4 \text{ (bottom)} + 9.52 \text{ (front/back)} + 1.7 \text{ (sides)}$
* Total = $12.62$

Area: $12.62 \text{ m}^2$

---

4) Closed Cube

* Dimensions: Side length = $5 \frac{1}{2}$ cm.
* A cube has 6 identical square faces.
* Decimal side length: $5.5$ cm.

Step 1: Find the area of one face.
* Area = $5.5 \times 5.5 = 30.25 \text{ cm}^2$

Step 2: Multiply by 6 (for all faces).
* Total Surface Area = $30.25 \times 6$
* Calculation: $30 \times 6 = 180$ and $0.25 \times 6 = 1.5$. So, $180 + 1.5 = 181.5$.

Area: $181.5 \text{ cm}^2$ (or $181 \frac{1}{2} \text{ cm}^2$)

---

5) Open Cuboid

* Dimensions: Length = $10 \frac{1}{2}$ in, Width = $2 \frac{1}{2}$ in, Height = $6 \frac{1}{4}$ in.
* Decimals: $L = 10.5$, $W = 2.5$, $H = 6.25$.
* It is open, so we need: Bottom + 2 Front/Back + 2 Sides.

Step 1: Calculate the Bottom Base.
* Area = $10.5 \times 2.5 = 26.25 \text{ in}^2$

Step 2: Calculate the Walls.
* Front and Back ($L \times H$): $10.5 \times 6.25 = 65.625$.
* Two of them: $65.625 \times 2 = 131.25 \text{ in}^2$.
* Side Walls ($W \times H$): $2.5 \times 6.25 = 15.625$.
* Two of them: $15.625 \times 2 = 31.25 \text{ in}^2$.

Step 3: Add them all together.
* Total = $26.25 + 131.25 + 31.25$
* $26.25 + 131.25 = 157.5$
* $157.5 + 31.25 = 188.75$

Area: $188.75 \text{ in}^2$ (or $188 \frac{3}{4} \text{ in}^2$)

---

6) Closed Cuboid

* Dimensions: Length = $5.2$ cm, Width = $3.5$ cm, Height = $12.6$ cm.

Step 1: Find the area of the three pairs of faces.
* Top and Bottom ($L \times W$): $5.2 \times 3.5 = 18.2 \text{ cm}^2$.
* Front and Back ($L \times H$): $5.2 \times 12.6 = 65.52 \text{ cm}^2$.
* Left and Right sides ($W \times H$): $3.5 \times 12.6 = 44.1 \text{ cm}^2$.

Step 2: Add them up and multiply by 2.
* Sum: $18.2 + 65.52 + 44.1 = 127.82$
* Total Surface Area: $127.82 \times 2 = 255.64$

Area: $255.64 \text{ cm}^2$

──────────────────────────────────────

Final Answer:
1) 169.5 in²
2) 802 cm²
3) 12.62 m²
4) 181.5 cm²
5) 188.75 in²
6) 255.64 cm²