A TP dog bed is in the shape of a triangle pyramid how much fabric is needed to make a TP given the following dimensions
The slant height of the equilateral triangle faces is 25 inches
The height of the base triangle is 26 inches
The base of the equilateral triangle is 30 inches
To calculate the fabric needed to make a TP dog bed, we need to first find the area of each equilateral triangle face and the area of the base triangle.
1. Area of equilateral triangle face:
The formula for the area of an equilateral triangle is A = (sqrt(3)/4) * s^2, where s is the side length of the equilateral triangle.
Given that the slant height of the equilateral triangle face is 25 inches, we can find the side length by using the Pythagorean theorem:
s = sqrt((25^2) - (26/2)^2)
s = sqrt(625 - 169)
s = sqrt(456)
s ≈ 21.35 inches
Now, we can calculate the area of one equilateral triangle face:
A = (sqrt(3)/4) * (21.35)^2
A ≈ 381.86 square inches
Since there are 4 equilateral triangle faces on a TP pyramid, the total area of the equilateral triangle faces is:
Total area = 4 * 381.86 square inches
Total area ≈ 1527.44 square inches
2. Area of base triangle:
The formula for the area of a triangle is A = (base * height) / 2.
Given that the base of the equilateral triangle is 30 inches and the height of the base triangle is 26 inches, we can calculate the area of the base triangle:
A = (30 * 26) / 2
A = 390 square inches
Now, the total fabric needed to make the TP dog bed is the sum of the area of the equilateral triangle faces and the area of the base triangle:
Total fabric needed = Total area + Area of base triangle
Total fabric needed ≈ 1917.44 square inches
Therefore, approximately 1917.44 square inches of fabric is needed to make a TP dog bed with the given dimensions.