How to find the surface area of a polyhedron - PSAT Math
Card 1 of 14
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?
Tap to reveal answer
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.
Tap to reveal answer
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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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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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
← Didn't Know|Knew It →
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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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
← Didn't Know|Knew It →
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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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
← Didn't Know|Knew It →
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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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
← Didn't Know|Knew It →
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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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
← Didn't Know|Knew It →
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?
Tap to reveal answer
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
← Didn't Know|Knew It →
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.
Tap to reveal answer
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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