Case1: The area of the isosceles trapezoid is 67.03 cm²
Case2: The area of the isosceles trapezoid is 50.41 cm²
Disclaimer:
In the question, it is not clear which is the value of the base and which is the value of the legs.
Case1:
Longer base a = 15.5 cm, shorter base b = 5.7 cm, and legs c = 8 cm.
Case2:
Longer base a = 15.5 cm, shorter base b = 8 cm, and legs c = 5.7 cm.
The formula to find out the area of an isosceles trapezoid is:
A = ½(a + b) * h
Here a and b are the bases of the trapezoid, and h is the height of the trapezoid.)
First, we need to find out the height of the trapezoid using base and legs values.
The height of the trapezoid is h = √{c² - (a - b)²/4}
Case1:
h = √{(8)²- ((15.5 - 5.7)²/4)}
⇒ h = √{(8)² - ((9.8)²/4)}
⇒ h = 6.32 cm
Therefore, the area of the isosceles trapezoid is
A = 1/2 × (a + b) × h
⇒ A = 1/2 × (15.5 + 5.7 ) × 6.32
⇒ A = 1/2 × 21.2 × 6.32
⇒ A = 67.03 cm²
Case2:
h = √{(5.7)²- ((15.5 - 8)²/4)}
⇒ h = √{(5.7)² - ((7.5)²/4)}
⇒ h = 4.29 cm
Therefore, the area of the isosceles trapezoid is
A = 1/2 × (a + b) × h
⇒ A = 1/2 × (15.5 + 8 ) × 4.29
⇒ A = 1/2 × 23.5 × 4.29
⇒ A = 50.41 cm²
Learn more about the area of the trapezoid at:
https://brainly.com/question/3953649
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