Question

Please answer all of them with a clear answer

Answer 1

See below for the solution to the questions

The parallel side of the trapezoid

The given parameters are:

Area = 138

a = 4x - 1

b = x - 4

Height = 12

The area is calculated as:

Area = 0.5 * (a + b) * height

So, we have:

0.5 *(4x - 1 + x - 4) * 12 = 138

This gives

5x - 5 = 23

Add 5 to both sides

5x = 28

Divide by 5

x = 5.6

Recall that:

a = 4x - 1 = 4 * 5.6 - 1 = 21.4

b = x - 4 = 5.6 - 4 =  1.6

Hence,  the short base length is 1.6 meters and the long base length is 21.4 meters

The largest angle in the triangle

The sides are given as:

x = 22

y = 24

z = 25

The largest angle always opposite the largest side.

This means that the largest angle is Z

The Circumference

The radius is given as:

r = 29

The circumference is calculated as:

$C = 2\pi r$

So, we have:

$C = 2\pi *29$

Evaluate

C = 182.21

Hence, the circumference is 182.21 inches

Measure of angle from arc

The measure of the arc is given as:

$\theta = 69^o$

The angle LIK is calculated as:

$m\angle LIK = \frac{\theta}2$

So, we have:

$m\angle LIK = \frac{69^o}2$

Evaluate the quotient

$m\angle LIK = 34.5^o$

Hence, the measure of the angle is $m\angle LIK = 34.5^o$

Read more about trapezoid at:

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Read more about circumference at:

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Read more about triangle at:

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