Here are the step-by-step calculations to find the surface area for each 3D figure.
1. Rectangular Prism
To find the surface area, we calculate the area of all six rectangular faces and add them together. The dimensions given are Length = 5 in, Width = 4 in, and Height = 3 in.
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Top and Bottom faces: $5 \text{ in} \times 4 \text{ in} = 20 \text{ sq in}$. Since there are two, $20 \times 2 = 40 \text{ sq in}$.
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Front and Back faces: $5 \text{ in} \times 3 \text{ in} = 15 \text{ sq in}$. Since there are two, $15 \times 2 = 30 \text{ sq in}$.
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Left and Right side faces: $4 \text{ in} \times 3 \text{ in} = 12 \text{ sq in}$. Since there are two, $12 \times 2 = 24 \text{ sq in}$.
Total Surface Area: $40 + 30 + 24 = 94 \text{ sq in}$.
2. Triangular Prism
This shape has two triangular bases and three rectangular sides.
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Triangular Bases: The base of the triangle is 6 ft and the height is 4 ft.
* Area of one triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 4 = 12 \text{ sq ft}$.
* Since there are two triangles: $12 \times 2 = 24 \text{ sq ft}$.
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Rectangular Sides: The prism has a length of 8 ft. The three rectangles correspond to the three sides of the triangle (6 ft, 5 ft, and 5 ft).
* Bottom rectangle: $6 \text{ ft} \times 8 \text{ ft} = 48 \text{ sq ft}$.
* Two side rectangles: $5 \text{ ft} \times 8 \text{ ft} = 40 \text{ sq ft}$ each. So, $40 \times 2 = 80 \text{ sq ft}$.
Total Surface Area: $24 + 48 + 80 = 152 \text{ sq ft}$.
3. Rectangular Pyramid
This shape has one rectangular base and four triangular faces that meet at a point.
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Rectangular Base: The dimensions are 6 m by 4 m.
* Area = $6 \times 4 = 24 \text{ sq m}$.
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Triangular Faces (Front and Back): These triangles have a base of 6 m and a slant height of 5 m.
* Area of one = $\frac{1}{2} \times 6 \times 5 = 15 \text{ sq m}$.
* For two triangles: $15 \times 2 = 30 \text{ sq m}$.
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Triangular Faces (Left and Right): These triangles have a base of 4 m and a slant height of 6 m.
* Area of one = $\frac{1}{2} \times 4 \times 6 = 12 \text{ sq m}$.
* For two triangles: $12 \times 2 = 24 \text{ sq m}$.
Total Surface Area: $24 + 30 + 24 = 78 \text{ sq m}$.
Final Answer:
1. Rectangular Prism:
94 sq in
2. Triangular Prism:
152 sq ft
3. Rectangular Pyramid:
78 sq m
Parent Tip: Review the logic above to help your child master the concept of solid nets worksheet answers.
