Question

How does one do 25? I dont know how to do it

Answer 1

Check the picture below.

so the prism is really two triangles, with a base of 9.8 and a height of 5.33, and then three rectangles

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{two triangles} }{2\left[ \cfrac{1}{2}(\underset{b}{9.8})(\underset{h}{5.33}) \right]}~~ + ~~\stackrel{\textit{front rectangle}}{(9.8)(3.8)}~~ + ~~\stackrel{\textit{left rectangle}}{(6.2)(3.8)}~~ + ~~\stackrel{\textit{right rectangle}}{(8.5)(3.8)}} \\\\\\ 52.234~~ + ~~37.25~~ + ~~23.56~~ + ~~32.3 ~~ \approx ~~ \text{\LARGE 145.3}~ft^2`

Answer 2

145.3 ft²

Explanation:

You want the surface area of the triangular prism shown.

Area

The surface of the prism consists of 5 faces:

• 3 rectangles
• 2 triangle

The dimensions required to find the areas of these are given in the diagram.

Rectangle area

The area of a rectangle is the product of its length and width. All of the rectangles shown have a height of 3.8 ft, so their total area is ...

lateral area = (3.8 ft)(9.8 ft) +(3.8 ft)(8.5 ft) +(3.8 ft)(6.2 ft)

= (3.8 ft)(9.8 +8.5 +6.2 ft) . . . . . . . factoring out 3.8 ft

You will recognize this as the product of the height of the prism and the perimeter of the triangular base.

Triangle area

The area of one triangle base is ...

A = (1/2)bh

The base is given as 9.8 ft, and the height is given as 5.33 ft, so the area is ...

A = (1/2)(9.8 ft)(5.33 ft)

There are two such triangular faces, so their total area is ...

base area = 2(1/2)(9.8 ft)(5.33 ft)

base area = (9.8 ft)(5.33 ft)

Total

The total surface area is the sum of the areas of the 5 faces:

surface area = rectangle area + base area

= (3.8 ft)(9.8 +8.5 +6.2 ft) +(9.8 ft)(5.33 ft) = 145.334 ft²

The surface area of the prism is about 145.3 ft².

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Additional comment

The surface area of any figure is the sum of the areas of the various surfaces that make it up. For polygonal prisms, the lateral area is made of rectangles. The total base area is the sum of the areas of the two polygonal bases. Here the bases are triangular, so the triangle area formula is used.

For figures such as cylinders, or cylinders with conical or hemispherical ends, you use the appropriate formulas for lateral area and spherical area, as needed.

It is usually helpful to memorize or keep handy the formulas for areas of various plane and curved figures.