Solve for X: Trapezoid Area of 78 cm² with Sides (X+10) and (12X-10)

Question

The area of the trapezoid in the diagram is 78 cm².

Calculate X.

00:00 Find X

00:03 We'll use the formula for calculating trapezoid area

00:07 (Sum of bases(AB+DC) multiplied by height(H))divided by 2

00:13 We'll substitute appropriate values according to the given data and solve for X

00:31 We'll group the numbers as one factor and X as another factor

00:42 We'll divide 6 by 2

00:53 We'll isolate X

01:04 And this is the solution to the problem

To solve this problem, we need to apply the area formula for a trapezoid:

The area $A$ of a trapezoid is given by $A = \frac{1}{2} \times (b_1 + b_2) \times h$ where $b_1$ and $b_2$ are the base lengths, and $h$ is the height.

The problem provides:

Substitute these into the area formula:

$78 = \frac{1}{2} \times ((X + 10) + (12X - 10)) \times 6$

Simplify the expression:

$78 = \frac{1}{2} \times (13X) \times 6$

Multiply through by 2 to clear the fraction:

$156 = 13X \times 6$

Simplify further:

$156 = 78X$

Solving for $X$ gives:

$X = \frac{156}{78}$

$X = 2$

Therefore, the solution to the problem is $X = 2$ .

$2$