The measure of one of the smaller base angles of an isosceles trapezoid is $60^\circ$. The shorter base is 5 inches long and the altitude is $2 \sqrt{3}$ inches long. What is the number of inches in the perimeter of the trapezoid?
The answer is 22, it's easy to figure out of you know about 30 60 90 triangles and im too lazy to write the work
+129846 Let the shorter base be at the top of the trapezoid
If we draw a perpendicular from the top right vertex to the longer base....we will form a 30-60-90 right triangle
The altitude = 2sqt 3
The right side of the trapezoid = 2sqrt (3) * 2/sqrt( 3 ) = 4
And remaining side = 2 = (longer base - shorter base) / 2
The perimeter is
Top base + 2 (sides) + [ longer base ]
5 + 2(4) + [ 5 + 2 (2) ] =
22
