Other Polyhedrons - PSAT Math
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A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.
The total surface area of a given regular icosahedron is 400 square centimeters. To the nearest tenth of a centimeter, what is the length of each edge?
A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.
The total surface area of a given regular icosahedron is 400 square centimeters. To the nearest tenth of a centimeter, what is the length of each edge?
The total surface area of the icosahedron is 400 square centimeters; since the icosahedron comprises twenty congruent faces, each has area 
square centimeters.
The area of an equilateral triangle is given by the formula
Set 
and solve for 
:
centimeters.
The total surface area of the icosahedron is 400 square centimeters; since the icosahedron comprises twenty congruent faces, each has area
The area of an equilateral triangle is given by the formula
Set
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A regular octahedron has eight congruent faces, each of which is an equilateral triangle.
A given octahedron has edges of length five inches. Give the total surface area of the octahedron.
A regular octahedron has eight congruent faces, each of which is an equilateral triangle.
A given octahedron has edges of length five inches. Give the total surface area of the octahedron.
The area of an equilateral triangle is given by the formula
Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is
Substitute 
:
square inches.
The area of an equilateral triangle is given by the formula
Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is
Substitute
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The above depicts a rectangular swimming pool for an apartment. 80% of the pool is six feet deep, and the remaining part of the pool is four feet deep. How many cubic feet of water does the pool hold?
The above depicts a rectangular swimming pool for an apartment. 80% of the pool is six feet deep, and the remaining part of the pool is four feet deep. How many cubic feet of water does the pool hold?
The cross-section of the pool is the area of its surface, which is the product of its length and its width:
square feet.
Since 80% of the pool is six feet deep, this portion of the pool holds
cubic feet of water.
Since the remainder of the pool - 20% - is four feet deep, this portion of the pool holds
cubic feet of water.
Add them together: the pool holds
cubic feet of water.
The cross-section of the pool is the area of its surface, which is the product of its length and its width:
Since 80% of the pool is six feet deep, this portion of the pool holds
Since the remainder of the pool - 20% - is four feet deep, this portion of the pool holds
Add them together: the pool holds
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