a metalworker is creating decorative points in the form of a triangular pyramid to go on top of a fence she is building she wants to know the surface area of each pyramid ise surface area formula to find the surface area of each pyramid based on figure 9.5cm 13.1cm 18.2cm 5.1cm
To find the surface area of a triangular pyramid, we need to calculate the areas of its individual faces and then sum them up.
The given measurements are as follows:
Base length (b) = 9.5 cm
Height of each triangular face (h) = 13.1 cm
Slant height from each corner of the base to the apex (s) = 18.2 cm
Height from the base to the apex of the pyramid (H) = 5.1 cm
First, let's find the area of the triangular base.
Area of a triangle (A) = (1/2) * base * height
A = (1/2) * 9.5 cm * 13.1 cm
A = 61.825 cm²
Now, we will calculate the area of each triangular face (3 in total) using the slant height and the height.
To find the base length of each triangular face, we can use the Pythagorean theorem:
Base length of each face (b') = √(s² - h²)
b' = √(18.2 cm² - 13.1 cm²)
b' = √(332.24 cm² - 171.61 cm²)
b' = √(160.63 cm²)
b' = 12.67 cm
Now, calculate the area of each face:
Area of each face (A') = (1/2) * b' * h
A' = (1/2) * 12.67 cm * 13.1 cm
A' = 82.9935 cm² (rounded to four decimal places)
Finally, calculate the total surface area of the pyramid by summing up the areas of all the faces:
Total surface area = Area of base + Area of each face * number of faces
Total surface area = 61.825 cm² + 82.9935 cm² * 3
Total surface area = 61.825 cm² + 248.9805 cm²
Total surface area = 310.8055 cm² (rounded to four decimal places)
Therefore, the surface area of the triangular pyramid is approximately 310.8055 cm².
wrong
Apologies for the mistake.
To find the surface area of a triangular pyramid, we need to calculate the areas of its individual faces.
The given measurements are as follows:
Base length (b) = 9.5 cm
Height of each triangular face (h) = 13.1 cm
Slant height from each corner of the base to the apex (s) = 18.2 cm
Height from the base to the apex of the pyramid (H) = 5.1 cm
First, let's find the area of the triangular base.
Area of a triangle (A) = (1/2) * base * height
A = (1/2) * 9.5 cm * 13.1 cm
A = 61.825 cm²
Next, we calculate the lateral area of the pyramid, which is the sum of the areas of the triangular faces.
Lateral area = (1/2) * perimeter of the base * slant height
The perimeter of the base (P) can be found by adding all three sides of the base:
P = 3 * 9.5 cm
P = 28.5 cm
Lateral area = (1/2) * 28.5 cm * 18.2 cm
Lateral area = 260.19 cm²
Finally, to find the total surface area, we add the area of the base to the lateral area:
Total surface area = Area of base + Lateral area
Total surface area = 61.825 cm² + 260.19 cm²
Total surface area = 322.015 cm²
Therefore, the surface area of the triangular pyramid is approximately 322.015 cm².