Find the area of the isosceles trapezoid with lower base 18cm, legs 6cm and base angles 30 degrees
To have a triangle the sum of any two sides must be greater than the third side
6+6 is not greater than 18
Your triangle cannot exist.
The coordinates of the vertices of a polygon are R(-4, 3), S(-4, -7), T(5, -7), and V(5, 3). Find the area and determine whether it is a parallelogram, rectangle, or square.
To find the area of an isosceles trapezoid, we can use the formula:
Area = (1/2) * (a + b) * h
where 'a' and 'b' are the lengths of the parallel bases and 'h' is the height of the trapezoid.
In this case, we are given the following:
Lower base (b1) = 18 cm
Legs (a1 and a2) = 6 cm
Base angles (θ) = 30 degrees
First, let's calculate the length of the upper base (b2). The isosceles trapezoid has equal-length legs, so both a1 and a2 are 6 cm.
Using the formula for the length of the upper base in an isosceles trapezoid:
b2 = b1 - 2 * (a1 * tan(θ))
Substituting the given values:
b2 = 18 cm - 2 * (6 cm * tan(30 degrees))
Now, we can calculate the value of tan(30 degrees):
tan(30 degrees) = (1 / √3)
Substituting this value into the equation:
b2 = 18 cm - 2 * (6 cm * (1 / √3))
Now, simplify the expression:
b2 = 18 cm - 12 cm / √3
To get rid of the square root in the denominator, multiply the numerator and the denominator by (√3):
b2 = 18 cm - (12 cm * √3) / 3
Now, simplify further:
b2 = 18 cm - 4 cm * √3
Finally, the formula for the area of the trapezoid becomes:
Area = (1/2) * (b1 + b2) * h
Given that the height (h) of the trapezoid is not provided, we cannot compute the area using the given information alone.