There is a triangle shaped pyramid with sides 6 cm base 8 cm and height 7cm. If I enlarge it using scale ratio of 1.2. What is the new perimeter and area of the new triangle pyramid? Please help. Thank you
I assume you can find the perimeter and area of the original pyramid.
if the sides double, so does the perimeter.
But the area, since it is the product of two sides, grows by a factor of 2^2, so it is 4 times as big.
To find the new perimeter and area of the enlarged pyramid, we need to consider how the scaling affects each dimension.
First, let's find the new dimensions of the triangle pyramid using the scale ratio of 1.2.
The new base length can be found by multiplying the original base length by the scale ratio.
New base length = 8 cm * 1.2 = 9.6 cm
Similarly, the new height can be found by multiplying the original height by the scale ratio.
New height = 7 cm * 1.2 = 8.4 cm
Now let's calculate the new slant height of the triangle pyramid using the Pythagorean theorem.
The slant height is the hypotenuse of a right triangle formed by the original height, half of the base, and the slant height itself.
Slant height = √( (0.5 * base)^2 + height^2 )
Original slant height = √( (0.5 * 8 cm)^2 + 7 cm^2 )
Original slant height ≈ √( 4 cm^2 + 49 cm^2 ) ≈ √( 53 cm^2 ) ≈ 7.28 cm
The new slant height can be found by multiplying the original slant height by the scale ratio.
New slant height = 7.28 cm * 1.2 ≈ 8.74 cm
Now that we have the new base length, new height, and new slant height, we can calculate the new perimeter and area of the triangle pyramid.
Perimeter of a triangle pyramid = Base length + 3 * Slant height
New perimeter = 9.6 cm + 3 * 8.74 cm ≈ 9.6 cm + 26.22 cm ≈ 35.82 cm
Area of a triangle pyramid = (Base length * Slant height) / 2
New area = (9.6 cm * 8.74 cm) / 2 ≈ 83.76 cm²
Therefore, the new perimeter of the enlarged triangle pyramid is approximately 35.82 cm, and the new area is approximately 83.76 cm².