Answer: 36
Step-by-step explanation:
The legs are given to be :
3x - 1 and -x + 27
The base = 5x + 1
One of the properties of an isosceles triangle is that two sides are equal , that is the two legs are equal. This means that
3x - 1 = - x + 27
3x + x = 27 + 1
4x = 28
x = 7
To calculate the length of the base, substitute x = 7 into the length of the base given , that is
Length of the base = 5(7) + 1
L = 35 + 1
L = 36
The area of a trapezoid is calculated by the equation,
A = 0.5(b₁ + b₂)h
where b₁ and b₂ are the bases and h is the height. When we substitute the given expression for the dimensions in the given,
A = 0.5(4x + 2x)(x - 6)
A = 0.5(6x)(x - 6) = 3x² - 18
Thus, the answer is letter A.
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