Question

Write an equation or an inequality to model the real-life situation. The area \(A\) of a trapezoid is equal to one half times the sum of seven and nine, times a number \(h\) plus seven.

Short answer

The equation derived from the given real-life situation is \(A = 0.5 * (7 + 9) * (h + 7)\).

Step-by-step solution

Identify the known quantities

The area 'A' of the trapezoid, the bases of the trapezoid are seven units and nine units, and an unrealized height 'h'.

Real-life situation to formula translation

Translate the given English statement into a mathematical formula. The area of a trapezoid is given by \(A = 0.5 * (b1 + b2) * h\), where 'b1' and 'b2' are the lengths of the bases of the trapezoid and 'h' is the height of the trapezoid. From the statement, we infer that 'b1' is 7, 'b2' is 9, and 'h' is implicitly 'h + 7'.

Write the equation

Substitute the known quantities into the formula to form an equation. Therefore, \(A = 0.5 * (7 + 9) * (h + 7)\).