Lesson 4 Homework Practice Surface Area Of Prisms Answers

How to Find the Surface Area of Triangular Prisms: Lesson 4 Homework Practice

A triangular prism is a three-dimensional shape that has two congruent triangles as its bases and three rectangles as its lateral faces. The surface area of a triangular prism is the sum of the areas of all six faces. To find the surface area, we need to know the dimensions of the base triangle and the height of the prism.

In this lesson, we will learn how to use the formula for the surface area of a triangular prism: SA = bh + (s1 + s2 + s3)H, where b and h are the base and height of the triangle, s1, s2, and s3 are the lengths of the three sides of the triangle, and H is the height of the prism. We will also practice applying this formula to some examples and check our answers using online resources.

Example 1

Find the surface area of the triangular prism shown below. Round to the nearest tenth if necessary.

Solution:

We can use the formula SA = bh + (s1 + s2 + s3)H to find the surface area. First, we need to identify the dimensions of the base triangle and the height of the prism.

The base of the prism is a right triangle with legs 5.6 cm and 3.8 cm. We can use the Pythagorean theorem to find the hypotenuse: s1 = sqrt(5.6^2 + 3.8^2) = 6.7 cm.

The height of the triangle is 3.8 cm.

The other two sides of the triangle are 4.2 cm and 6.4 cm.

The height of the prism is 8 cm.

Now we can plug these values into the formula:

SA = bh + (s1 + s2 + s3)H

SA = (5.6)(3.8) + (6.7 + 4.2 + 6.4)(8)

SA = 21.28 + (17.3)(8)

SA = 21.28 + 138.4

SA = 159.68

The surface area of the triangular prism is about 159.7 cm^2.

Example 2

Find the surface area of the triangular prism shown below. Round to the nearest tenth if necessary.

Solution:

We can use the same formula SA = bh + (s1 + s2 + s3)H to find the surface area. First, we need to identify the dimensions of the base triangle and the height of the prism.

The base of the prism is a right triangle with legs 9 m and 12 m. The hypotenuse is s1 = sqrt(9^2 + 12^2) = 15 m.

The height of the triangle is 12 m.

The other two sides of the triangle are also 15 m each.

The height of the prism is 10 m.

Now we can plug these values into the formula:

SA = bh + (s1 + s2 + s3)H

SA = (9)(12) + (15 + 15 + 15)(10)

SA = 108 + (45)(10)

SA = 108 + 450SA = 558

The surface area of the triangular prism is 558 m^2.

Check Your Answers

To check your answers, you can use online calculators or worksheets that provide the solutions. Here are some links that you can use to verify your work:

Lesson 4 Skills Practice Surface Area of Triangular Prisms

Surface Area of Triangular Prisms | Decimals - Answer Key

Triangular Prism Calculator

Conclusion

In this lesson, we learned how to find the surface area of triangular prisms using the formula SA = bh + (s1 + s2 + s3)H. We also practiced applying this formula to some examples and checked our answers using online resources. We hope this lesson helped you understand how to calculate the surface area of triangular prisms and improve your math skills. 66dfd1ed39

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