what is an area of an isosceles trapezoid if the length of its shorter base is 18 cm, the length of an altitude is 9 cm, and the measure of the acute angle is 45.
i need answer asap pls
Answers
Answer:
draw the isosceles trapezoid
draw the altitude from the left top vertex and also draw the altitude from the top right vertex
this forms two right triangles, one on the left and one on the right
the bottom left acute angle is 45º (as is the other acute angle)
one leg is the altitude of 9 cm
the other leg is not known
the hypotenuse is also not known but it is not needed to solve the problem
use the tan function
tan=opposite/adjacent
tan45º=9/x where x=the unknown leg
x=9/tan45º
tan45º=1
x=9/1
x=9 cm
the same reasoning applies to the triangle on the right side
you have a rectangle 9 by 18 and a right triangle on each end
the bottom base is 18 cm + 9cm + 9cm=36 cm (you are adding the two bottom bases from the two right triangles to the length of the top trapezoidal base to get the bottom trapezoidal base)
A=(1/2)(h)(B+b)
A=(1/2)(9)(36+18)
A=(1/2)(9)(54)
A=(1/2)(486)
A=243 square cm is the area of the trapezoid
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