Question

Find the area of each triangle.

   Find the area of each triangle.

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 1, Problem 45

Instant Answer

Solved by Expert Laura Skalaski

04/27/2020

Step 1

Step 1: We start by writing down the formula for the area of a triangle, which is given by: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Show more…

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Key Concepts

Triangle Area Calculation

This concept involves determining the area of a triangle using mathematical formulas that relate its dimensions. The area is a measure of the surface enclosed by the triangle, and the most common formula is ½ times the base times the height.

Base and Height

The base and height are fundamental dimensions in the calculation of a triangle's area. The base refers to any chosen side of the triangle, while the height is the perpendicular distance from the base to the opposite vertex. This relationship is central to the ½ × base × height area formula.

Heron’s Formula

Heron’s formula provides an alternative method for calculating the area of a triangle when the lengths of all three sides are known. It involves computing the semi-perimeter (half of the sum of the side lengths) and then finding the square root of the product of the semi-perimeter and its differences with each side.

Geometric Reasoning

Geometric reasoning involves using spatial relationships and properties of shapes to deduce measurements and solve problems. In the context of finding a triangle's area, it includes identifying key dimensions such as the base, height, or side lengths that are critical for applying the correct formula.

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