Trapezoid Area Problem: Express Area with Height 2X and Parallel Sides (X+14) and (3X+7)

Question

Express the area of the trapezoid by X

00:00 Express the area of the trapezoid using X

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

00:06 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2

00:16 We'll substitute appropriate values according to the given data and solve for the area

00:31 We'll simplify what we can

00:37 We'll group the numbers as one factor and X as another factor

00:41 We'll properly distribute - multiply each factor by X

00:47 And this is the solution to the question

To express the area of the trapezoid in terms of $X$ , follow these steps:

Step 1: Identify the given values for the trapezoid's dimensions. The top base $b_1$ is $X + 14$ , the bottom base $b_2$ is $3X + 7$ , and the height $h$ is $2X$ .
Step 2: Use the trapezoid area formula $A = \frac{1}{2} \times (b_1 + b_2) \times h$ .
Step 3: Compute the sum of the bases: $(X + 14) + (3X + 7) = X + 14 + 3X + 7 = 4X + 21$ .
Step 4: Calculate the area using the formula: $A = \frac{1}{2} \times (4X + 21) \times (2X)$ .
Step 5: Simplify: $A = \frac{1}{2} \times (4X + 21) \times 2X = (4X + 21) \times X$ .
Step 6: Simplify further by distributing: $A = 4X^2 + 21X$ .

Thus, the area of the trapezoid expressed in terms of $X$ is $4X^2 + 21X$ .

$4x^2+21x$