Question

side $cd$ of rectangle $abcd$ measures 12 meters, as shown. each of the three triangles with a side along segment $cd$ is an equilateral triangle. what is the total area of the shaded regions? express your answer in simplest radical form.

Answer 1

The area of the shaded region is 8√3 m².

Here we have to find the total area of the shaded regions.

The three triangles along CD are all equilateral and they all have the same height, so they are all congruent to each other.

The length of each side of these three triangles = 12/3

                                                                                  = 4m

We know that an angle along line CD between two 60° angles = 180° - 60° - 60°

                                                                                                         = 60°

So the two shaded triangles are also equilateral triangles with a side length of 4m.

The area of shaded the region = 2× ( area of one shaded triangle)

                                             = 2 ×( 1/2 × base × height)

                                            = 2×( 1/2 × 4×2√3)

                                            = 8√3 meter²

Therefore we get an area of the shaded part 8√3.

To know more about the triangle refer to the link given below:

https://brainly.com/question/17335144

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