The smaller base of the isosceles trapezoid is 8 cm, the lateral side is 10 cm

| August 11, 2021 | education

The smaller base of the isosceles trapezoid is 8 cm, the lateral side is 10 cm, and the acute angle at the base is 46 degrees. Find an indication of this isosceles trapezoid

Given:
isosceles trapezoid ABCE,
BC = 8 centimeters,
AE = 10 centimeters,
angle A = angle E = 45 degrees.
Find the perimeter of an isosceles trapezoid -?
Solution:
1. Consider an isosceles trapezoid ABCE. Let’s draw the heights of the VN and SK.
2. Triangle BHA = triangle СKE by hypotenuse and acute angle, since CE = AB, angle A = angle E. Then AH = KE = (AE – НK): 2 = (10 – 8): 2 = 2: 2 = 1 centimeter.
3. Consider the triangle ABН. Knowing that the sum of the degree measures of the angles is 180 degrees. Then AВН = (180 – 90 – 45) = 45 (degrees). So the triangle ABН is isosceles, AH = BH = 1 centimeter.
4. Perimeter, that is, P ABCE = 1 + 1 + 8 + 10 = 20 (centimeters).
Answer: 20 centimeters.



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