Question

Olivia goes to Egypt and saw a model of a triangular shaped pyramid. She enlarged it using a scale factor of 1.2. What will be the perimeter and area of the new triangle pyramid.

Answer 1

Area 33.6 and perimeter 24

Answer 2

1) 28.8 cm 2) 134.05 cm²

Explanation:

1) Since it is a Triangular Shaped Pyramid its lateral area is made up of three triangles and another one in the base. Moreover, to that, we can see it's an isosceles triangle. The scale factor will dilate the pyramid, to another one 1.2 times bigger.

Perimeter only makes sense on plane figures, so when we talk of Pyramid Perimeter we are talking about the Base Perimeter, an Equilateral Triangle whose legs measure 8 cm.

Base Perimeter = 8+8+8 =24 cm

Multiplied by 1.2 (scale factor)

New Base Perimeter = 28.8 cm

2) Area

The Area of this new Pyramid is the sum of Lateral area and Base Area of a Triangular Pyramid.

`A=(bh)/(2)\\ (8*7)/(2)=\\(56)/(2) =28`cm² There are 3 triangles over the base, so Lateral Area=84cm²

Base Area=
`(8^(2)√(3))/(4) =16√(3)`

Total Area = 84 +16
`√(3)` cm²≈111.71 cm²

Multiplied by 1.2

New Total Area = (110.8 +19.2
`√(3)`) ≈ 134.05 cm²