Question

solving a real - world application problem
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 = $

Explanation:

Step1: Find height of one triangle

Use Pythagorean theorem. Let the base of one isosceles triangle be $b = 2$ cm and the leg be $l=5$ cm. The height $h$ of an isosceles triangle can be found by dividing the base in half ($\frac{b}{2}=1$ cm) and applying the Pythagorean theorem $h=\sqrt{l^{2}-(\frac{b}{2})^{2}}=\sqrt{5^{2}-1^{2}}=\sqrt{25 - 1}=\sqrt{24}=2\sqrt{6}$ cm.

Step2: Calculate area of one triangle

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. So, $A_{1}=\frac{1}{2}\times2\times2\sqrt{6}=2\sqrt{6}$ square - centimeters.

Step3: Calculate total area of the spinner

Since the spinner is made up of two congruent isosceles triangles, $A_{total}=2\times A_{1}=4\sqrt{6}\approx4\times2.4495 = 9.798$ square - centimeters.

Step4: Calculate the cost

The cost per square - centimeter is $13.25$. So the total cost $C=13.25\times A_{total}=13.25\times9.798\approx13.25\times9.8 = 129.85$.

Answer:

$129.85$