Let's solve the problem step by step for both solid figures shown in the worksheet.
---
Problem 1: Rectangular Prism
Given Dimensions:
- Length = 10 in
- Width = 3 in
- Height = 6 in
####
Step 1: Draw the Net
A rectangular prism has 6 faces:
- 2 bases (top and bottom): each is a rectangle of 10 in × 3 in
- 2 side faces: each is 10 in × 6 in
- 2 end faces: each is 3 in × 6 in
The net would consist of these six rectangles arranged so they can fold into a box.
####
Step 2: Calculate Surface Area
Surface Area = Sum of areas of all faces
Break it down:
- Top and Bottom: $2 \times (10 \times 3) = 2 \times 30 = 60$ in²
- Front and Back: $2 \times (10 \times 6) = 2 \times 60 = 120$ in²
- Left and Right: $2 \times (3 \times 6) = 2 \times 18 = 36$ in²
Add them up:
$$
60 + 120 + 36 = 216 \text{ in}^2
$$
✔ Surface Area of Rectangular Prism = 216 square inches
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Problem 2: Square Pyramid
Given Dimensions:
- Base is a square with side = 8 ft
- Slant height = 10 ft (from apex to midpoint of base edge)
> Note: The diagram shows triangular faces with slant height = 10 ft, and base = 8 ft.
####
Step 1: Draw the Net
The net of a square pyramid includes:
- One square base (8 ft × 8 ft)
- Four congruent triangles (each with base 8 ft and height 10 ft)
Arrange the four triangles around the square base.
####
Step 2: Calculate Surface Area
Total Surface Area = Area of Base + Lateral Surface Area
1.
Area of Base:
$$
8 \times 8 = 64 \text{ ft}^2
$$
2.
Area of One Triangular Face:
$$
\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 10 = 40 \text{ ft}^2
$$
3.
Total Area of Four Triangles:
$$
4 \times 40 = 160 \text{ ft}^2
$$
4.
Total Surface Area:
$$
64 + 160 = 224 \text{ ft}^2
$$
✔ Surface Area of Square Pyramid = 224 square feet
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✔ Final Answers:
1.
Rectangular Prism:
- Net: 6 rectangles (two of 10×3, two of 10×6, two of 3×6)
-
Surface Area = 216 in²
2.
Square Pyramid:
- Net: 1 square (8×8) and 4 triangles (base 8 ft, height 10 ft)
-
Surface Area = 224 ft²
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Let me know if you'd like a visual sketch description or help drawing the nets!
Parent Tip: Review the logic above to help your child master the concept of surface area nets worksheet pdf.
