The picture shows the layout of a
regular triangular
pyramid. Calculate
how many square
centimeters of paper
are needed to make
this pyramid. Provide
the answer to the
nearest square
centimeter.

Answers:  

Explanation:

Part (a)

A regular triangular pyramid, aka regular tetrahedron, has all four triangles that are identical copies of one another. They are congruent triangles. This will apply to part (b) as well.

To find the area of one of the triangles, we'll use the formula

A = 0.25*sqrt(3)*x^2

where x is the side length. This formula applies to equilateral triangles only.

In this case, x = 20, so

A = 0.25*sqrt(3)*x^2

A = 0.25*sqrt(3)*20^2

A = 173.20508 approximately

That's the area of one triangle, but there are four total, so the entire area is about 4*173.20508 = 692.82032 which rounds to 693 sq cm.

The units "sq cm" can be written as "cm^2".

Part (b)

We'll use the same idea as part (a). But the formula to find the area of one triangle is much simpler.

The area of one of the triangles is A = 0.5*base*height = 0.5*6*4 = 12 sq cm.

So the area of all four triangles combined is 4*12 = 48 sq cm

This area is exact.

The area of each 2D flat net corresponds exactly to the surface area of each 3D pyramid. This is because we can cut the figure out and fold along the lines to form the 3D shapes.

answer: plz put a pic in so i can answer it

step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°