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. 2 congruent isosceles triangles are connected by their bases. A circle is drawn around the triangles. 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

The total cost of the two to make this part of the compass will be equal to $129.85.

Given to us

The base of the isosceles Triangle = 2 cm

The length of the legs of the triangle = 5 cm

The metal used to construct the spinner costs $13. 25 per square centimeter,

What is the area of a single isosceles triangle?

We know that the area of a triangle can be written as,

$\rm Area =\sqrt{s(s-a)(s-b)(s-c)}$

where the value of s is $\dfrac{a+b+c}{2}$.

Substitute the value,

$s=\dfrac{5+5+2}{2} = 6$

Area of the triangle

$\rm Area =\sqrt{6(6-5)(6-5)(6-2)} = 4.8989 \approx 4.9\ cm^2$

What is the area of two isosceles triangles?

We already know the area of an isosceles triangle, therefore the area of the two isosceles triangles will be 9.8 cm².

how much will it cost to make this part of the compass?

The cost to make this part of the compass will be equal to,

9.8 x $13.25 = $129.85

Hence, the total cost of the two to make this part of the compass will be equal to $129.85.

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