Question

find a simplified expression to represent the area of the triangle. the area formula for a triangle is (\frac{1}{2}bh), where (b) is the base and (h) is the height. the expression that represents the area of this triangle is (square x^2 + square x + square) (cm^2). ((2x + 12)) cm ((4x - 2)) cm image of right triangle

Explanation:

Step1: Identify base and height

Base \( b = (4x - 2) \) cm, Height \( h = (2x + 12) \) cm.

Step2: Apply area formula

Area \( A=\frac{1}{2}bh=\frac{1}{2}(4x - 2)(2x + 12) \).

Step3: Expand the product

First, multiply \( (4x - 2)(2x + 12) \):
\( 4x\times2x + 4x\times12 - 2\times2x - 2\times12 = 8x^{2}+48x - 4x - 24 = 8x^{2}+44x - 24 \).

Step4: Multiply by \(\frac{1}{2}\)

\( A=\frac{1}{2}(8x^{2}+44x - 24)=4x^{2}+22x - 12 \).

Answer:

The expression is \( 4x^{2}+22x - 12 \) \( \text{cm}^2 \), so the boxes are filled with \( 4 \), \( 22 \), and \( -12 \) respectively.