ATP dog bed is in the shape of a triangular pyramid how much fabric is needed to make a TP given the following dimensions the slant height of the quadrilateral triangular faces is 25 inches. The height and of the base triangle is 26 inches the base of these quadrilateral triangular triangles is 30 inches.
To calculate the amount of fabric needed to make a triangular pyramid (TP) with the given dimensions, we need to find the total surface area of the shape.
First, let's calculate the area of the base triangle:
Area of base triangle = (1/2) * base * height
Area of base triangle = (1/2) * 30 * 26
Area of base triangle = 15 * 26
Area of base triangle = 390 square inches
Next, let's calculate the lateral area of the triangular faces:
Lateral area of each triangular face = (1/2) * base * slant height
Lateral area of each triangular face = (1/2) * 30 * 25
Lateral area of each triangular face = 15 * 25
Lateral area of each triangular face = 375 square inches
Since the triangular pyramid has 3 identical triangular faces, the total lateral area is:
Total lateral area = 3 * 375
Total lateral area = 1125 square inches
Finally, to find the total surface area of the triangular pyramid, add the base area and the lateral area:
Total surface area = base area + total lateral area
Total surface area = 390 + 1125
Total surface area = 1515 square inches
Therefore, you would need 1515 square inches of fabric to make a triangular pyramid with the given dimensions.