The value of x in the trapezoid given, to the nearest tenth, is: 10.5.
What is a Trapezoid?
A trapezoid is a quadrilateral that has two sides only that are parallel to each other.
What is the Area of a Trapezoid?
To find the area of a trapezoid, the formula used is expressed as: 1/2(a + b) × h, where:
- a and b are length of the two base sides that are parallel.
- h is the height of altitude of the trapezoid.
Given the following:
Area of trapezoid = 174 units²
AP = 6
PB = x + 3
CD = 2x + 6
AC = 10
Using the formula, we variables in the formula are:
a = AP + PB = 6 + x + 3 = x + 9
b = CD = 2x + 3
h = PC = √(AC² - AP²)
h = √(10² - 6²) = 8
Plug in the values into 1/2(a + b) × h:
174 = 1/2(x + 9 + 2x + 3) × 8
174 = 1/2(3x + 12) × 8
174 = (3x + 12) × 4
174 = 12x + 48
174 - 48 = 12x
126 = 12x
126/12 = x
10.5 = x
x = 10.5
Learn more about the trapezoid on:
https://brainly.com/question/1463152
#SPJ1
