Answer :
The area of the trapezoid is 22√30 square centimeters.
To find the area of a trapezoid, you can use the formula:
Area = (1/2) * (sum of the lengths of the bases) * (height)
In your case, the bases are 4 cm and 18 cm, and the height is not given. To calculate the height, you can use the Pythagorean theorem, as the trapezoid can be divided into a rectangle and two right triangles.
First, calculate the length of the trapezoid's altitude (height):
Height^2 = Side^2 - (1/2 * Base Difference)^2
Height^2 = 13^2 - (1/2 * (18 - 4))^2
Height^2 = 169 - (1/2 * 14)^2
Height^2 = 169 - 7^2
Height^2 = 169 - 49
Height^2 = 120
Height = √120
Height = 2√30 cm
Now that you have the height, you can find the area of the trapezoid:
Area = (1/2) * (4 + 18) * 2√30
Area = (1/2) * 22 * 2√30
Area = 22√30 square cm
So, the area of the trapezoid is 22√30 square centimeters.
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Answer:
132 cm²
Step-by-step explanation:
h² = 13² - x²
h² = 15² - (14 - x)²
169 - x² = 225 - (196 - 28x + x²) = 29 + 28x -x²
28x = 169 - 29 = 140
x = 5
h = √13² - x² = √169 - 25=√144 = 12
Area of Trapezoid: (4 + 18) x 12 / 2 = 132
