In a rectangular trapezoid ABCD, the lateral side AB = 10 cm, the larger base AD
| June 20, 2021 | education
In a rectangular trapezoid ABCD, the lateral side AB = 10 cm, the larger base AD = 18 cm, the angle D is 45 degrees. Find the area of this trapezoid.
From the top of the obtuse angle C we draw the height CH. Quadrangle ABCН is a rectangle since CH is height, and the trapezoid is rectangular. Then AB = CH = 10 cm, and BC = AН.
In a right-angled triangle СDН, one of its acute angles is 45, then this triangle is isosceles and right-angled, and DН = СН = 10 cm.
Then the length of the segment AH = AD – DH = 18 – 10 = 8 cm, then BC = AH = 8 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * СН / 2 = (8 + 18) * 10/2 = 130 cm2.
Answer: The area of the trapezoid is 130 cm2.
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