Question

a section of a rectangle is shaded. the area of the shaded section is 63 square units. what is the value of x? 9 units 11 units 18 units 21 units

Explanation:

Step1: Recall trapezoid area formula

The shaded shape is a right trapezoid. Its area formula is $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1=7$, $b_2=x$, $h=7$, and $A=63$.

Step2: Substitute values into formula

$$63 = \frac{1}{2}(7 + x) \times 7$$

Step3: Simplify and solve for $x$

First, multiply both sides by 2:
$$126 = 7(7 + x)$$
Divide both sides by 7:
$$18 = 7 + x$$
Subtract 7 from both sides:
$$x = 18 - 7 = 11$$

Answer:

11 units