Find the missing dimensions of the triangular prism if the surface area is 912.1 square inches and the lateral area is 800.1 square inches.
Hint
Surface area equals the lateral area plus the area of both bases.
Answer
The height of the base triangle is 8 inches and the hypotenuse is about 16.1 inches.
Example 3
Find the lateral and surface area of the cylinder.
Hint
The circumference of a circle is 2πr and the area of a circle is πr2.
Answer
The lateral area is 6.28 square feet and the surface area is 7.85 square feet.
Example 4
Find the lateral and surface area of the trapezoidal prism.
Hint
Treat the trapezoids as a triangle and a rectangle glued together.
Answer
The lateral area is 1118.2 cm2 and the surface area is 1325.2 cm2.
Example 5
Find the radius and circumference of the circle at the base of the cylinder if the lateral area is 150 yd2. Then find the surface area.
Hint
The lateral area is equal to the circumference times the height of the cylinder.
Answer
The radius is about 3 yd, the circumference is approximately 18.8 yd, and the surface area is about 206.9 yd2.
Example 6
A regular dodecagon (12 sides) is the base of a prism of height 19 inches. If the lateral area of the prism is 228 square inches, what is the length of each side of the dodecagon?
Hint
The lateral area is equal to the perimeter of the base times the height of the prism.
Answer
Each of the dodecagon's sides is 1 inch long.
Example 7
Find the lateral and surface area of the triangular prism.
Hint
Treat the triangular base like two right triangles back-to-back.
Answer
The lateral area is about 895.6 m2 and the surface area is about 1122.7 m2.
Example 8
After the apocalyptic destruction of the forests, only one tree stump remains. You want to preserve it, so you decide to cover it in plastic wrap. What better way to preserve a dead tree? Assuming the stump is perfectly cylindrical with a height of 3 feet and a diameter of 2.4 feet, how much plastic wrap will you need to cover the top and sides of the stump?
Hint
You can't cover the bottom. That would be impressive, but impractical.
Answer
You'll need at least 27.1 square feet of plastic wrap to cover the tree stump.
Example 9
The Catfish Factory has gone out of business due to too much cat hair in their tuna. As a result, all the cat workers are homeless. Since these cats are so darn cute (and you're tired of them pooping on your driveway), you decide to buy them a big litter box. How much paper will you need to gift-wrap their new litter box?
Hint
The base is in the shape of a trapezoid. Treat this as a rectangle with two congruent triangles on either side.
