Question

what is the area of this trapezoid? 9 cm 12 cm 18 cm text alternative a) 162 cm² b) 189 cm² c) 135 cm² d) 324 cm²

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A = \frac{(a + b)}{2} \times h$, where $a$ and $b$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases).

Step2: Identify the values

From the diagram, the two bases are $a = 9\ \text{cm}$ and $b = 18\ \text{cm}$, and the height $h = 12\ \text{cm}$.

Step3: Substitute into the formula

First, calculate the sum of the bases: $a + b = 9 + 18 = 27\ \text{cm}$.

Then, multiply by the height and divide by 2: $A = \frac{27}{2} \times 12$.

Simplify the calculation: $\frac{27 \times 12}{2} = 27 \times 6 = 162$? Wait, no, wait. Wait, $27\times12 = 324$, then divide by 2: $324\div2 = 162$? Wait, no, wait, let's check again. Wait, $9 + 18 = 27$, then $\frac{27}{2} \times 12 = 27 \times 6 = 162$? But wait, the options have 162 as option A, but wait, maybe I made a mistake. Wait, no, let's recalculate. Wait, $a = 9$, $b = 18$, $h = 12$. So $A = \frac{(9 + 18)}{2} \times 12 = \frac{27}{2} \times 12 = 27 \times 6 = 162$. Wait, but let me check the options again. Option A is 162, B is 189, C is 135, D is 324. Wait, but maybe I misread the diagram. Wait, the height is 12, the top base is 9, bottom base is 18. So the formula is correct. So the area should be 162? Wait, but let me check again. Wait, $ (9 + 18) = 27$, times 12 is 324, divided by 2 is 162. Yes, that's correct. So the answer is A? Wait, but wait, maybe the height is different? No, the diagram shows height 12. So the calculation is correct.

Answer:

A) $162\ \text{cm}^2$