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Bianca calculated the height of the equilateral triangle with side lengths of 10. Then, she used the formula for area of a triangle to approximate its area, as shown below. Calculate the area of the equilateral triangle using the formula for area of a regular polygon, and compare it to Bianca’s answer. The apothem, rounded to the nearest tenth, is ---units. The perimeter of the equilateral triangle is ---units. Therefore, the area of the equilateral triangle is---- , or approximately 43.5 units2. The calculated areas are---

Respuesta :

The apothem of a equilateral triangle is the short leg of a special triangle (30-60-90).

  • The apothem of the triangle is 2.9 units.
  • The perimeter of the equilateral triangle is 30 units.
  • The area of the equilateral triangle is 43.5 squared units.
  • The calculated areas of both are same instead of using the different formulas.

Given information-

The side of the triangle is 10 units.

The apothem, rounded to the nearest tenth.

Apothem of a equilateral triangle

The apothem of a equilateral triangle is the short leg of a special triangle (30-60-90). It can be given as,

[tex]s=\dfrac{\sqrt{3} a}{6} \\ [/tex]

Here [tex]a[/tex] is the side of the triangle.

Put the values,

[tex]s=\dfrac{\sqrt{3} \times10}{6} \\\\ s=\dfrac{10\sqrt{3} }{6} \\ s=2.88[/tex]

Thus the apothem of the triangle is 2.9 units.

2)  Perimeter of the equilateral triangle-

Perimeter of the equilateral triangle is the equal to the three times of the sides. Thus the perimeter [tex]p[/tex] of the given triangle is,

[tex]p=3\times10\\ p=30[/tex]

Thus the perimeter of the equilateral triangle is 30 units.

3) The area of the equilateral triangle-

The area of the regular polygon is can be given as,

[tex]A=\dfrac{1}{2} \times h\times p [/tex]

Put the values,

[tex]A=\dfrac{1}{2} \times 2.9\times 30\\ A=43.5[/tex]

Thus the area of the equilateral triangle is 43.5 squared units.

4)The calculated areas-

The calculated areas of both are same instead of using the different formulas.

  • The apothem of the triangle is 2.9 units.
  • The perimeter of the equilateral triangle is 30 units.
  • The area of the equilateral triangle is 43.5 squared units.
  • The calculated areas of both are same instead of using the different formulas.

Learn more about the apothem here;

https://brainly.com/question/10580427