SOLUTION: Two cardboard pieces in the form of equilateral triangles having a side of 3cm each are symmetrically glued to form a regular star.the area of the star.

Question 924425: Two cardboard pieces in the form of equilateral triangles having a side of 3cm each are symmetrically glued to form a regular star.the area of the star.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The superimposed part is a hexagon,
and it is surrounded by six small equilateral triangles that form the points of the star.
Because it is all so symmetrical, the sides of all the little equilateral triangles,
and the sides of the hexagon
are all congruent.
Since three such sides add up to a side of the large triangles,
the sides of the small triangles measure .
The area of the star is the area of one of the large triangles plus the area of 3 small triangles/star points.
The area of a triangle is calculated as

Since all these triangles are equilateral,
, and
.
So the are of each triangle is
.
For the large triangle, the area is
.
For each small triangle, the area is

So the total area of the star is
===
RELATED QUESTIONS
The figure shows how 201cm cubes are glued together to form a solid find the surface area (answered by Alan3354)

Theo is building a garden against his house. He bought two pieces of wood that are each... (answered by greenestamps)

A rectangular piece of cardboard with perimeter 30 in., two parallel and equally spaced... (answered by ankor@dixie-net.com)

You’re given a side length of 7 centimeters. How many equilateral triangles can you... (answered by josgarithmetic)

Mid-points of the side of an equilateral triangle of side 18 cm are joined to form... (answered by fcabanski)

A side of an equilateral triangle is 10 cm. the midpoints of its sides are joined to form (answered by reviewermath)

A rectangular piece of cardboard is to be formed into an uncovered box. The piece of... (answered by checkley77)

A rectangular piece of cardboard is to be formed into an uncovered box. The piece of... (answered by ankor@dixie-net.com)

A rectangular piece of cardboard is to be formed into an uncovered box. The piece of... (answered by macston)