In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit.
a = 14 meters, b = 12 meters, c = 4 meters

검증된 단계별 안내

Identify the side lengths of the triangle: \(a = 14\) meters, \(b = 12\) meters, and \(c = 4\) meters.

Calculate the semi-perimeter \(s\) of the triangle using the formula: \(s = \frac{a + b + c}{2}\).

Substitute the values of \(a\), \(b\), and \(c\) into the semi-perimeter formula to find \(s\).

Apply Heron's formula to find the area \(A\) of the triangle: \(A = \sqrt{s(s - a)(s - b)(s - c)}\).

Substitute the values of \(s\), \(a\), \(b\), and \(c\) into Heron's formula and simplify under the square root to find the area before rounding.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Heron's Formula

Heron's formula calculates the area of a triangle when the lengths of all three sides are known. It uses the semi-perimeter, s = (a + b + c) / 2, and the area is found by √[s(s - a)(s - b)(s - c)]. This method avoids needing the height or angles.

Semi-perimeter of a Triangle

The semi-perimeter is half the perimeter of a triangle, calculated as s = (a + b + c) / 2. It is a key intermediate value in Heron's formula, simplifying the area calculation by incorporating all three side lengths into one term.

Rounding and Units in Measurement

After calculating the area, it is important to round the result to the nearest whole number as specified. Additionally, the units of area are the square of the length units (e.g., square meters), reflecting the two-dimensional nature of area.

In Exercises 25–30, use Heron's formula to find the area of each triangle. Round to the nearest square unit.a = 14 meters, b = 12 meters, c = 4 meters