An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. What is the area of the equilateral triangle, rounded to the nearest tenth?
A. 2.7 cm^2
B. 4.1 cm^2
C. 16.2 cm^2
D. 24.2 cm^2
Answer (1)
Analyze the given data: apothem = 2.16 cm, perimeter = 22.45 cm.
Apply the formula: A re a = 2 1 × P er im e t er × A p o t h e m .
Substitute the given values: A re a = 2 1 × 22.45 × 2.16 = 24.246 .
Round the result to the nearest tenth: 24.2 c m 2 .
Explanation
Problem Analysis We are given an equilateral triangle with an apothem of 2.16 cm and a perimeter of 22.45 cm. Our goal is to find the area of this triangle, rounded to the nearest tenth.
Area Formula The area of an equilateral triangle can be calculated using the formula: A re a = 2 1 ∗ P er im e t er ∗ A p o t h e m where the perimeter is the sum of the lengths of all three sides, and the apothem is the distance from the center of the triangle to the midpoint of a side.
Substitute Values We are given the perimeter as 22.45 cm and the apothem as 2.16 cm. Plugging these values into the formula, we get: A re a = 2 1 ∗ 22.45 ∗ 2.16
Calculate Area Now, we perform the calculation: A re a = 2 1 ∗ 22.45 ∗ 2.16 = 24.246
Round to Nearest Tenth Finally, we round the area to the nearest tenth: A re a ≈ 24.2 c m 2
Final Answer Therefore, the area of the equilateral triangle, rounded to the nearest tenth, is 24.2 c m 2 .
Examples
Equilateral triangles are commonly found in architecture and design. For example, consider designing a mosaic pattern using equilateral triangular tiles. Knowing the apothem and perimeter allows you to quickly calculate the area each tile covers, helping you estimate the number of tiles needed for a specific area. This calculation ensures efficient material usage and accurate project planning.
