Question

How Do you solve this?

Answer 1

660 cm²

(last answer choice)

Explanation:

The triangular prism consists of the following two different surface shapes(triangles and rectangles) \

2 triangles each of height 12 cm and base 5 cm

Since area of each triangle = 1 bh the area of the two triangular sides
= 2 x 1/2bh = bh = 5 x 12 = 60 cm²

The rectangular surface at the bottom has dimensions 5 cm x 20 cm
Area of this rectangular surface = 5 x 20 = 100 cm²

The vertical side of the prism is a rectangle with dimensions 12cm x 20 cm
Area of this rectangle = 12 x 20 = 240 cm²

The other surface is an inclined rectangle with length = 20 cm
To find the width use the dimensions of the triangle to find the hypotenuse which is the length

`\sf{hypotenuse = √(12^2 + 5^2) = √(144+25) = √(169) = 13 \;cm}`

Area of the inclined rectangle
= 13 x 20 = 260 cm²

Total surface area = 60 + 100 + 240 + 260 = 660 cm²

Answer 2

D. 660 cm²

Explanation:

You want the total surface area of the right triangular prism with triangle legs of 5 and 12 cm, and a 20 cm distance between the bases.

Base area

In order to solve this, we must assume the triangular bases are right triangles. The area of each of them is ...

A = 1/2bh

A = 1/2(5 cm)(12 cm) = 30 cm²

Then the total base area is ...

2A = 2·30 cm² = 60 cm²

Lateral area

In order to find the lateral area, we need to know the length of the hypotenuse of the triangular base. The Pythagorean theorem tells us it is ...

h = √(5² +12²) = √169 = 13

Then the perimeter of the base is 5 +12 +13 cm = 30 cm.

Each edge of the base is one side of a rectangular face whose other dimension is 20 cm. Then the total lateral area is ...

LA = Ph

LA = (30 cm)(20 cm) = 600 cm²

Surface area

The total surface area of the prism is the sum of the base areas and the lateral area:

SA = B + LA = 60 cm² +600 cm² = 660 cm²

The total surface area of the triangular prism is 660 cm².

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Additional comment

You may recognize the right triangle as having sides of the lengths in the Pythagorean triple {5, 12, 13}.