Calculate Rectangle Area: Finding Area of (a+3) by (b+8)

Calculate the area of the rectangle below in terms of a and b.

Let us begin by reminding ourselves of the formula to calculate the area of a rectangle: width X length

$S=w⋅h$

When:

S = area

w = width

h = height

We take data from the sides of the rectangle in the figure.$w=b+8$$h=a+3$

We then substitute the above data into the formula in order to calculate the area of the rectangle:

$S=w⋅h = (b+8)(a+3)$

We use the formula of the extended distributive property:

$(a+b)(c+d)=ac+ad+bc+bd$

We substitute once more and solve the problem as follows:

$S=(b+8)(a+3)=(b)(a)+(b)(3)+(8)(a)+(8)(3)$

$(b)(a)+(b)(3)+(8)(a)+(8)(3)=ab+3b+8a+24$

Therefore, the correct answer is option B: ab+8a+3b+24.

Keep in mind that, since there are only addition operations, the order of the terms in the expression can be changed and, therefore,

$ab+3b+8a+24=ab+8a+3b+24$