the area of an isosceles trapezoid is 77 square inches the height measures for inches and the legs are 5 inches long find the length of the bases
Answers
lengths of bases are 16.25 , 22.25 inches
The area of a trapezoid is 77 square inches, the height measures 4 inches and the legs are 5 inches long. Find the length of the bases.
arrangements are shown in figure,
we know, in isosceles trapezoid, its height and congruent side form a right angled triangle.
so, from ∆ADL,
5² = 4² + DL²
⇒DL = 3 inches.
similarly, MC = 3 inches.
now area of trapezium = 1/2 (sum of parallel sides) × height
⇒77 = 1/2 × (AB + DC) × 4
⇒77/2 = (AB + LM + 2 × 3inches )
⇒77/2 = (AB + AB + 6) [ because, AB = LM ]
⇒38.5 = 2AB + 6
⇒AB = 32.5/2 = 16.25 inches
then, DC = AB + 6 inches
= 16.25 + 6 = 22 inches
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