Question

Pls help. !!!!!!!!!!!!!!!!!! (Give steps if you can)

Answer 1

Answer:

$144 cm^{2}$

Step-by-step explanation:

Step 1: Find the true length of each side

We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of $x$, then we get the true length of each side, so we would get $5x, 12x, 6x, 5x$ for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation $5x + 12x + 6x + 5x = 56$. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:

AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm  

Step 2: Calculate the Height

Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: $\frac{base_{1} + base_2}{2}*height$. So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.

Step 3: Calculate the Area

Lastly, we can calculate the area. The formula is $\frac{base_{1} + base_2}{2}*height$. In this case, the numbers would be $\frac{12 + 24}{2} * 8 = 144cm^{2}$

I know this is a lot, so let me know if you have any questions!