To find the surface area of a triangular pyramid with the given net, we first need to find the individual areas of each face.
1. Base Triangle:
Area = 1/2 * base * height
Area = 1/2 * 14.7 ft * 13.8 ft
Area = 101.43 sq ft
2. Side Triangle 1:
To find the height of the side triangle, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Where a and b are the sides of the triangle and c is the hypotenuse (17 ft).
Let x be the height of the side triangle:
x^2 + 13.8^2 = 17^2
x^2 = 17^2 - 13.8^2
x = √(17^2 - 13.8^2)
x ≈ 8.03 ft
Now we can find the area of the side triangle:
Area = 1/2 * base * height
Area = 1/2 * 14.7 ft * 8.03 ft
Area ≈ 59.14 sq ft
3. Side Triangle 2:
The side triangle 2 is the same as side triangle 1, so it has the same area:
Area ≈ 59.14 sq ft
Now we can find the total surface area of the triangular pyramid by adding the areas of the base triangle and two side triangles:
Total Surface Area = Base Area + 2 * Side Area
Total Surface Area = 101.43 sq ft + 2 * 59.14 sq ft
Total Surface Area ≈ 219.71 sq ft
Therefore, the surface area of the triangular pyramid represented by the given net is approximately 219.71 square feet.
triangle with a triangle smaller 14.7 ft, 17 ft, 13.8 ft
Find the surface area of a triangle pyramid represented by the given net
5 answers
wrong
I apologize for the error in my previous calculation. Let's try again:
The net of the triangular pyramid consists of 1 base triangle and 3 side triangles.
1. Base Triangle:
Area = 1/2 * base * height
Area = 1/2 * 14.7 ft * 13.8 ft
Area = 101.43 sq ft
2. Side Triangle 1:
Area = 1/2 * base * height
Area = 1/2 * 17 ft * 13.8 ft
Area = 117.3 sq ft
3. Side Triangle 2:
The side triangle 2 is the same as side triangle 1, so it has the same area:
Area = 117.3 sq ft
4. Side Triangle 3 (the smaller triangle within the net):
To find the area of the smaller triangle, we can use the same formula:
Area = 1/2 * base * height
Area = 1/2 * 14.7 ft * 13.8 ft
Area = 101.43 sq ft
Now we can find the total surface area of the triangular pyramid by adding the areas of all the faces:
Total Surface Area = Base Area + 3 * Side Area
Total Surface Area = 101.43 sq ft + 3 * 117.3 sq ft
Total Surface Area = 453.33 sq ft
Therefore, the correct surface area of the triangular pyramid represented by the given net is 453.33 square feet. Thank you for your understanding.
The net of the triangular pyramid consists of 1 base triangle and 3 side triangles.
1. Base Triangle:
Area = 1/2 * base * height
Area = 1/2 * 14.7 ft * 13.8 ft
Area = 101.43 sq ft
2. Side Triangle 1:
Area = 1/2 * base * height
Area = 1/2 * 17 ft * 13.8 ft
Area = 117.3 sq ft
3. Side Triangle 2:
The side triangle 2 is the same as side triangle 1, so it has the same area:
Area = 117.3 sq ft
4. Side Triangle 3 (the smaller triangle within the net):
To find the area of the smaller triangle, we can use the same formula:
Area = 1/2 * base * height
Area = 1/2 * 14.7 ft * 13.8 ft
Area = 101.43 sq ft
Now we can find the total surface area of the triangular pyramid by adding the areas of all the faces:
Total Surface Area = Base Area + 3 * Side Area
Total Surface Area = 101.43 sq ft + 3 * 117.3 sq ft
Total Surface Area = 453.33 sq ft
Therefore, the correct surface area of the triangular pyramid represented by the given net is 453.33 square feet. Thank you for your understanding.
Use the image to answer the question.
A net of a triangular prism is drawn unfolded and open. It shows a dashed line equilateral triangle in the center, with 3 triangles adjoined to the baselines of the central triangle.
A baseline of the central triangle is labeled as 17 feet. The perpendicular height of the central base triangle is 14.7 feet, drawn with a dotted line and a right angle symbol with the base. The perpendicular height of an adjoined triangle is shown as 13.8 feet, and is drawn with a dotted line and a right angle symbol with the base.
Find the surface area of a triangular pyramid represented by the given net.
(1 point)
A net of a triangular prism is drawn unfolded and open. It shows a dashed line equilateral triangle in the center, with 3 triangles adjoined to the baselines of the central triangle.
A baseline of the central triangle is labeled as 17 feet. The perpendicular height of the central base triangle is 14.7 feet, drawn with a dotted line and a right angle symbol with the base. The perpendicular height of an adjoined triangle is shown as 13.8 feet, and is drawn with a dotted line and a right angle symbol with the base.
Find the surface area of a triangular pyramid represented by the given net.
(1 point)
To find the surface area of the triangular pyramid represented by the given net, we need to calculate the area of each face.
Given:
- The central equilateral triangle has a base length of 17 feet and a height of 14.7 feet.
- The three adjoined triangles have a height of 13.8 feet.
1. Base Triangle:
The area of the central equilateral triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 ft * 14.7 ft
Area = 125.55 sq ft
2. Side Triangles:
The area of each adjoined triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 ft * 13.8 ft
Area = 117.3 sq ft
There are three of these side triangles, so the total area of all three side triangles is:
Total Side Area = 3 * 117.3 sq ft
Total Side Area = 351.9 sq ft
Now, we can find the total surface area of the triangular pyramid by adding the areas of the base triangle and the three side triangles:
Total Surface Area = Base Area + Total Side Area
Total Surface Area = 125.55 sq ft + 351.9 sq ft
Total Surface Area = 477.45 sq ft
Therefore, the surface area of the triangular pyramid represented by the given net is 477.45 square feet.
Given:
- The central equilateral triangle has a base length of 17 feet and a height of 14.7 feet.
- The three adjoined triangles have a height of 13.8 feet.
1. Base Triangle:
The area of the central equilateral triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 ft * 14.7 ft
Area = 125.55 sq ft
2. Side Triangles:
The area of each adjoined triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 ft * 13.8 ft
Area = 117.3 sq ft
There are three of these side triangles, so the total area of all three side triangles is:
Total Side Area = 3 * 117.3 sq ft
Total Side Area = 351.9 sq ft
Now, we can find the total surface area of the triangular pyramid by adding the areas of the base triangle and the three side triangles:
Total Surface Area = Base Area + Total Side Area
Total Surface Area = 125.55 sq ft + 351.9 sq ft
Total Surface Area = 477.45 sq ft
Therefore, the surface area of the triangular pyramid represented by the given net is 477.45 square feet.