Question

a spinner for a board game consists of a cardboard circle with two plastic arrows anchored to its center. the arrows are congruent isosceles triangles connected at their bases, as shown. the base of each triangle measures 2 centimeters and the perimeter of each triangle is 10 centimeters. what is the approximate total area of the plastic triangles on the spinner? herons formula: area = \\(\sqrt{s(s - a)(s - b)(s - c)}\\)

Explanation:

Step1: Find equal sides of triangle

Perimeter = 2a + base = 10 cm. Base = 2 cm, so 2a = 10 - 2 = 8 → a = 4 cm.

Step2: Calculate semi-perimeter (s)

s = perimeter/2 = 10/2 = 5 cm.

Step3: Apply Heron's formula for 1 triangle

Area = √[s(s - a)(s - b)(s - c)] = √[5(5 - 4)(5 - 4)(5 - 2)] = √(5×1×1×3) = √15 ≈ 3.87 cm².

Step4: Total area for 2 triangles

Total area = 2×3.87 ≈ 7.7 cm².

Answer:

C. 7.7 square centimeters