If a = 12 cm, b = 27 cm, c = 15 cm, and d = 20 cm, what is the area of the poster? (2 points) Responses 412 cm2 412 cm 2 462 cm2 462 cm 2 624 cm2 624 cm 2 474 cm2
First, we need to calculate the area of the rectangle formed by side a and side b.
Area = a * b = 12 cm * 27 cm = 324 cm^2
Next, we need to calculate the area of the triangle formed by side c, side d, and the diagonal connecting the two sides (hypotenuse of the right triangle).
To find the length of the diagonal, we can use the Pythagorean theorem:
d^2 = c^2 + d^2
d^2 = 15^2 + 20^2
d^2 = 225 + 400
d^2 = 625
d = √625
d = 25 cm
Now, we can calculate the area of the triangle using the formula for the area of a triangle:
Area = (1/2) * base * height
Area = (1/2) * 15 cm * 20 cm = 150 cm^2
Finally, we can find the total area of the poster by adding the areas of the rectangle and the triangle:
Total area = 324 cm^2 + 150 cm^2 = 474 cm^2
Therefore, the total area of the poster is 474 cm^2.