Question

The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.

If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.

Cost = $

Answer 1

just answered this question it was -> $129.82

Answer 2

$129.82

Explanation:

We are given that the figure is two isosceles triangles. Both triangles have a base of 2 cm and both have legs of 5 cm.

To find the area of a triangle, we use the formula A = 1/2bh, where b is the base of the triangle and h is the height.

We do not have the height of the triangles; we must use the Pythagorean theorem to find this.

A perpendicular line dropped from the vertex to the 2-cm base will cut this base in half. This gives us 1 as one leg, an unknown leg, and 5 as the hypotenuse. The Pythagorean theorem states "the sum of the squares of the two legs of a right triangle equals the sum of the hypotenuse"; or, algebraically,

a² + b² = c²

Substituting our known information, we have

a² + 1² = 5²

a² + 1 = 25

Subtracting 1 from each side,

a²+ 1 - 1 = 25 - 1

a² = 24

Taking the square root of each side, we have

`√(a^2)=√(24)\\\\a=\sqrt[24}=√(4* 6)=2√(6)`

Using our formula for area, we have

A = 1/2(2)(2√6) = 1(2√6) = 2√6

Since we have two identical triangles, the combined area is

2(2√6) = 4√6

This makes the total cost

4√6(13.25) = $129.82