4-20-20 Grade 7 Volume of a Triangular Prism Worksheet online ... - Free Printable

You're right to point out the confusion! The worksheet is titled "Surface Area of Prisms and Pyramids", but the figures shown are all triangular prisms. There are no pyramids on this page.

A triangular prism has:
* Two identical triangular bases.
* Three rectangular lateral faces connecting the corresponding sides of the triangles.

The surface area (SA) of a triangular prism is calculated as:
SA = 2 × (Area of one triangular base) + (Area of the three rectangular lateral faces)

We can also think of it as:
SA = 2 × (Base Area) + (Perimeter of Base × Height of Prism)

Let's solve each problem step-by-step.

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Problem 1

* Triangular Base: Right triangle with legs 2 ft and 2 ft.
* Height of Prism (length): 4 ft.

Step 1: Area of one triangular base
Since it's a right triangle, Area = (1/2) × base × height
= (1/2) × 2 ft × 2 ft = 2 ft²

Step 2: Area of two bases
2 × 2 ft² = 4 ft²

Step 3: Perimeter of the triangular base
We need the hypotenuse of the right triangle.
Hypotenuse = √(2² + 2²) = √8 = 2√2 ≈ 2.828 ft
Perimeter = 2 ft + 2 ft + 2.828 ft = 6.828 ft

Step 4: Lateral Surface Area (Perimeter × Height)
Lateral SA = 6.828 ft × 4 ft ≈ 27.312 ft²

Step 5: Total Surface Area
Total SA = 4 ft² + 27.312 ft² = 31.312 ft²

Rounded to nearest hundredth: 31.31 ft²

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Problem 2

* Triangular Base: Right triangle with legs 3 ft and 3 ft.
* Height of Prism: 6 ft.

Step 1: Area of one triangular base
Area = (1/2) × 3 ft × 3 ft = 4.5 ft²

Step 2: Area of two bases
2 × 4.5 ft² = 9 ft²

Step 3: Perimeter of the triangular base
Hypotenuse = √(3² + 3²) = √18 = 3√2 ≈ 4.243 ft
Perimeter = 3 ft + 3 ft + 4.243 ft = 10.243 ft

Step 4: Lateral Surface Area
Lateral SA = 10.243 ft × 6 ft ≈ 61.458 ft²

Step 5: Total Surface Area
Total SA = 9 ft² + 61.458 ft² = 70.458 ft²

Rounded to nearest hundredth: 70.46 ft²

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Problem 3

* Triangular Base: Base = 8 ft, Height = 6 ft. (Given perpendicular height)
* Slant height (side length of triangle) = 7.21 ft (This is likely the length of the equal sides if it's isosceles, but we'll use the given base and height for area).
* Height of Prism: 14 ft.

Step 1: Area of one triangular base
Area = (1/2) × base × height = (1/2) × 8 ft × 6 ft = 24 ft²

Step 2: Area of two bases
2 × 24 ft² = 48 ft²

Step 3: Perimeter of the triangular base
We have base = 8 ft.
The other two sides are given as 7.21 ft each (assuming isosceles triangle based on the diagram and value).
Perimeter = 8 ft + 7.21 ft + 7.21 ft = 22.42 ft

Step 4: Lateral Surface Area
Lateral SA = 22.42 ft × 14 ft = 313.88 ft²

Step 5: Total Surface Area
Total SA = 48 ft² + 313.88 ft² = 361.88 ft²

Rounded to nearest hundredth: 361.88 ft²

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Problem 4

* Triangular Base: Base = 8 ft, Height = 6 ft.
* Side lengths = 7.21 ft (same as Problem 3, likely isosceles).
* Height of Prism: 14 ft.

This is identical to Problem 3!

Total Surface Area = 361.88 ft²

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Problem 5

* Triangular Base: Base = 4 ft, Height = 3 ft.
* Slant height (side length) = 3.61 ft (likely the equal sides of an isosceles triangle).
* Height of Prism: 11 ft.

Step 1: Area of one triangular base
Area = (1/2) × 4 ft × 3 ft = 6 ft²

Step 2: Area of two bases
2 × 6 ft² = 12 ft²

Step 3: Perimeter of the triangular base
Assuming isosceles: Perimeter = 4 ft + 3.61 ft + 3.61 ft = 11.22 ft

Step 4: Lateral Surface Area
Lateral SA = 11.22 ft × 11 ft = 123.42 ft²

Step 5: Total Surface Area
Total SA = 12 ft² + 123.42 ft² = 135.42 ft²

Rounded to nearest hundredth: 135.42 ft²

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Problem 6

* Triangular Base: Right triangle with legs 2 ft and 2 ft.
* Height of Prism: 4 ft.

This is identical to Problem 1!

Total Surface Area = 31.31 ft²

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Problem 7

* Triangular Base: Base = 6, Height = 4. (Note: The "5" is likely the slant height or side length, not needed for area calculation since height is given).
* Height of Prism: 12.

Step 1: Area of one triangular base
Area = (1/2) × 6 × 4 = 12

Step 2: Area of two bases
2 × 12 = 24

Step 3: Perimeter of the triangular base
We have base = 6.
The other two sides are given as 5 and 5? (Looking at the diagram, it seems like an isosceles triangle with sides 5, 5, and base 6).
Perimeter = 6 + 5 + 5 = 16

Step 4: Lateral Surface Area
Lateral SA = 16 × 12 = 192

Step 5: Total Surface Area
Total SA = 24 + 192 = 216

Rounded to nearest hundredth: 216.00

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Problem 8

* Triangular Base: Right triangle with legs 2 and 2.
* Height of Prism: 4.

This is identical to Problems 1 and 6!

Total Surface Area = 31.31

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Problem 9

* Triangular Base: Right triangle with legs 2 and 2.
* Height of Prism: 4.

This is identical to Problems 1, 6, and 8!

Total Surface Area = 31.31

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## ✔ Final Answers:

1) 31.31 ft²
2) 70.46 ft²
3) 361.88 ft²
4) 361.88 ft²
5) 135.42 ft²
6) 31.31 ft²
7) 216.00
8) 31.31
9) 31.31

*(Note: Units are feet squared (ft²) for all problems unless otherwise specified.)*