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 the trapezoid area formula

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the parallel sides and \(h\) is the height. Here, \(a = 7\), \(b=x\), \(h = 7\), and \(A=63\).

Step2: Substitute values into the formula

Substitute into \(A=\frac{(a + b)h}{2}\), we get \(63=\frac{(7 + x)\times7}{2}\).

Step3: Solve the equation for \(x\)

First, multiply both sides by \(2\): \(63\times2=(7 + x)\times7\), so \(126=(7 + x)\times7\).
Then divide both sides by \(7\): \(\frac{126}{7}=7 + x\), \(18 = 7+x\).
Finally, subtract \(7\) from both sides: \(x=18 - 7=11\).

Answer:

11 units