I have a model of a triangle shaped pyramid with sides 6cm base 8cm and height 7cm. If I enlarge the pyramid using a scale factor of 1.2, what will the new perimeter and area be?
perimeter grows by a factor of 2, area by 4.
So, find the existing values and then scale them up.
To calculate the new perimeter and area of the enlarged pyramid, we need to first determine the dimensions of the enlarged pyramid.
The scale factor of 1.2 indicates that all the corresponding sides of the original pyramid will be multiplied by 1.2 to obtain the dimensions of the enlarged pyramid. Therefore, the dimensions of the enlarged pyramid will be:
Length of base: 8cm * 1.2 = 9.6cm
Length of each side: 6cm * 1.2 = 7.2cm
Height: 7cm * 1.2 = 8.4cm
Now that we have the dimensions of the enlarged pyramid, we can calculate the new perimeter and area.
Perimeter:
The perimeter is the sum of the lengths of all the sides of the pyramid. In this case, the base of the pyramid is a triangle, so the perimeter will be the sum of the lengths of the three sides of the base plus the length of the slant height (which can be calculated using the Pythagorean theorem).
Perimeter of the base = 8cm + 6cm + 6cm (since it is an isosceles triangle) = 20cm
Slant height = sqrt((8.4cm)^2 + (3.6cm)^2) = sqrt(70.56cm^2 + 12.96cm^2) = sqrt(83.52cm^2) = 9.14cm (rounded to 2 decimal places)
Perimeter of the enlarged pyramid = Perimeter of the base + sum of lengths of the sides = 20cm + 7.2cm + 7.2cm + 7.2cm + 9.14cm + 9.14cm + 9.14cm = 68.92cm (rounded to 2 decimal places)
Therefore, the new perimeter of the enlarged pyramid is approximately 68.92cm.
Area:
The area of a triangular pyramid can be calculated by finding the area of the base triangle and adding the areas of the three triangular faces.
Area of the base triangle = (1/2) * length of base * height = (1/2) * 8.4cm * 7cm = 29.4cm^2 (rounded to 1 decimal place)
Area of each triangular face = (1/2) * length of side * slant height = (1/2) * 7.2cm * 9.14cm = 32.958cm^2 (rounded to 3 decimal places)
Total area of the enlarged pyramid = Area of the base triangle + sum of the areas of the triangular faces = 29.4cm^2 + (3 * 32.958cm^2) = 128.274cm^2 (rounded to 3 decimal places)
Therefore, the new area of the enlarged pyramid is approximately 128.274cm^2.