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zhane2015
Group Title
5. In trapezoid PQRS, . Find the area of PQRS. Leave your answer in simplest radical form.
(1 point)
144 + 72sqrt3
72 + 72sqrt3
288sqrt3 – 216
144sqrt3 – 72
 one year ago
 one year ago
zhane2015 Group Title
5. In trapezoid PQRS, . Find the area of PQRS. Leave your answer in simplest radical form. (1 point) 144 + 72sqrt3 72 + 72sqrt3 288sqrt3 – 216 144sqrt3 – 72
 one year ago
 one year ago

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zhane2015 Group TitleBest ResponseYou've already chosen the best response.0
what's the formula??
 one year ago

nader1 Group TitleBest ResponseYou've already chosen the best response.1
With triangle RTQ, we see that angle T is 90° and angle R is 30°. Since the angles in a triangle always sum to 180°, angle Q is 180°  90°  30° = 60°. Thus, triangle RTQ is a 30°60°90° right triangle. The sides of a 30°60°90° triangle are in ratio 1:√3:2 (this is in the form (side opposite to 30° angle):(side opposite to 60° angle):(side opposite to 90° angle)). The hypotenuse, the side opposite opposite to the 90° angle, has a length of 24. The altitude of the triangle, the side opposite to the 30° angle, therefore has a length of 24/2 = 12; and the base of the triangle, the side opposite to the 60° angle, has a length of 12√3. Therefore, the area of PQRS is: (area of left trapezoid) + (area of triangle) = (1/2)(6 + 18)(12) + (1/2)(12√3)(12) = 144 + 72√3.
 one year ago
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