A net pattern has a square base of side lengths 3 inches, 3 inches, 3 inches, and 3 inches. The sides of the square base are attached to four congruent triangles with heights of 8... A net pattern has a square base of side lengths 3 inches, 3 inches, 3 inches, and 3 inches. The sides of the square base are attached to four congruent triangles with heights of 8 inches. Find the overall surface area.
Understand the Problem
The question describes a net pattern consisting of a square base with side length 3 inches and four congruent triangles attached to the sides of the square, each with a height of 8 inches. This arrangement describes a square pyramid. The question will likely ask to calculate the surface area or volume. Need more context to fully solve.
Answer
$57$ square inches
Answer for screen readers
The total surface area of the net is $57$ square inches.
Steps to Solve
- Identify the Shape
The net describes a square pyramid. It has a square base and four identical triangle faces.
- Calculate the Area of the Square Base
The area of a square is side length squared. $$Area_{square} = side^2$$ Given that the side length is 3 inches: $$Area_{square} = 3^2 = 9 \text{ square inches}$$
- Calculate the Area of One Triangle
The area of a triangle is $1/2 * base * height$. In this case, each triangle has a base of 3 inches (the side of the square) and a height of 8 inches. $$Area_{triangle} = \frac{1}{2} * base * height$$ $$Area_{triangle} = \frac{1}{2} * 3 * 8 = 12 \text{ square inches}$$
- Calculate the Total Area of the Four Triangles
Since there are four congruent triangles: $$Area_{4 triangles} = 4 * Area_{triangle} = 4 * 12 = 48 \text{ square inches}$$
- Calculate the Total Surface Area of the Net
The total surface area is the sum of the area of the square base and the total area of the four triangles. $$Area_{total} = Area_{square} + Area_{4 triangles}$$ $$Area_{total} = 9 + 48 = 57 \text{ square inches}$$
The total surface area of the net is $57$ square inches.
More Information
The net represents a square pyramid. Calculating the areas of each face and summing them gives the total surface area of the pyramid.
Tips
A common mistake is forgetting to multiply the area of a single triangle by four, since there are four triangles. Another mistake is to mix up the height of the triangle with the side length of the square.
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