Question

1. find the area of the triangle. $a = \frac{1}{2}bh$

the triangle has a base labeled $x + 8$ and a height labeled $2x + 3$

Explanation:

Step1: Identify base and height

Base $b = x+8$, Height $h = 2x+3$

Step2: Substitute into area formula

$A = \frac{1}{2}(x+8)(2x+3)$

Step3: Expand the binomials

$(x+8)(2x+3) = x(2x)+x(3)+8(2x)+8(3) = 2x^2+3x+16x+24 = 2x^2+19x+24$

Step4: Multiply by $\frac{1}{2}$

$A = \frac{1}{2}(2x^2+19x+24)$

Answer:

$x^2 + \frac{19}{2}x + 12$