# By cutting it into 10 congruent right angled triangles, work out the area of a regular pentagon of perimeter 80cm.

1
by lefebvre

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by lefebvre

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Since the perimeter is 80cm, the length of one side is 80/5 = 16cm. When we draw a straight line from the vertices to the median of the opposite side, we form ten triangles. We just need to focus on one. Please refer to the figure attached.

We know that the length of the base is 16/2 = 8cm. We let the height be a.

This would mean that:

tan(54°)=a/8

We just get the decimal approximation:

1.3764 = a/8

1.3764*8 = a

11.0112 = a

The area of the pentagon is 10 times the area of the triangle:

10[8*11.0112/2] = 10[44.0448] = 440.448 cm²

We know that the length of the base is 16/2 = 8cm. We let the height be a.

This would mean that:

tan(54°)=a/8

We just get the decimal approximation:

1.3764 = a/8

1.3764*8 = a

11.0112 = a

The area of the pentagon is 10 times the area of the triangle:

10[8*11.0112/2] = 10[44.0448] = 440.448 cm²