Question

find the area of the triangle.
(triangle area = \\( \frac { 1 } { 2 } \cdot \text { base } \cdot \text { height } \\) )
the area of the triangle is \\( \square \\)
(simplify your answer.)

Explanation:

Step1: Identify base and height

Base of triangle is \((8x - 7)\) inches, height is \(4x\) inches.

Step2: Apply triangle area formula

Area formula: \(\frac{1}{2} \times \text{base} \times \text{height}\). Substitute values: \(\frac{1}{2} \times (8x - 7) \times 4x\).

Step3: Simplify the expression

First, multiply \(\frac{1}{2}\) and \(4x\): \(\frac{1}{2} \times 4x = 2x\). Then multiply by \((8x - 7)\): \(2x(8x - 7) = 16x^2 - 14x\).

Answer:

The area of the triangle is \(16x^2 - 14x\) square inches.