Surface area worksheet for calculating the area of mixed geometric shapes.

Since I can't view or access uploaded images directly, I can't see the specific shapes or dimensions in your image. However, I can help you solve surface area problems for common 3D shapes if you describe them or provide their dimensions.

Here’s a general guide to solving surface area problems for the most common 3D shapes typically found in such worksheets:

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🔷 1. Triangular Prism (Shape A)

- Surface Area = 2 × (Area of triangular base) + (Perimeter of triangle) × height of prism
- Formula:
$$
SA = 2 \times \left(\frac{1}{2} \times b \times h\right) + (a + b + c) \times H
$$
where:
- $b$ = base of triangle,
- $h$ = height of triangle,
- $a, b, c$ = side lengths of triangle,
- $H$ = height (length) of prism

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🔷 2. Rectangular Pyramid (Shape B)

- Surface Area = Area of base + Sum of areas of triangular faces
- Formula:
$$
SA = l \times w + \frac{1}{2} \times l \times s_1 + \frac{1}{2} \times w \times s_2 + \frac{1}{2} \times l \times s_3 + \frac{1}{2} \times w \times s_4
$$
But more simply:
$$
SA = lw + \frac{1}{2}(pl)
$$
where:
- $l, w$ = length and width of base,
- $p$ = perimeter of base,
- $s$ = slant height (depends on which face)

> Often, each triangular face is calculated separately using $ \frac{1}{2} \times \text{base} \times \text{slant height} $

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🔷 3. Cone (Shape C)

- Surface Area = Base area + Lateral surface area
- Formula:
$$
SA = \pi r^2 + \pi r l
$$
where:
- $r$ = radius of base,
- $l$ = slant height

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🔷 4. Cylinder (Shape D)

- Surface Area = 2 × Base area + Lateral surface area
- Formula:
$$
SA = 2\pi r^2 + 2\pi r h
$$
where:
- $r$ = radius,
- $h$ = height

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🔷 5. Cube (Shape E)

- All sides equal.
- Formula:
$$
SA = 6s^2
$$
where $s$ = side length

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🔷 6. Square Pyramid (Shape F)

- Base is square; 4 congruent triangular faces.
- Formula:
$$
SA = s^2 + 2sl
$$
where:
- $s$ = side of square base,
- $l$ = slant height

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🔷 7. Rectangular Prism (Shape G)

- Formula:
$$
SA = 2(lw + lh + wh)
$$
where:
- $l$ = length,
- $w$ = width,
- $h$ = height

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🔷 8. Hemisphere (Shape H)

- Surface area includes curved part + flat circular base
- Formula:
$$
SA = 2\pi r^2 + \pi r^2 = 3\pi r^2
$$

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🔷 9. Triangular Prism (Shape I)

- Same as Shape A — two triangular bases and three rectangular faces
- Use same formula as above

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✔ Tips:

- Always check units — ensure all measurements are in the same unit.
- Round to nearest tenth if required.
- Label each shape carefully.

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👉 If you can describe the shapes and give the dimensions, I’ll walk you through each one step by step!

For example:
> "Shape A is a triangular prism with base 6 cm, height 4 cm, and length 10 cm..."

Let me know!