Arc CD is Two-thirds of the circumference of a circle. What is the radian measure of the central angle? StartFraction 2 pi Over 3 EndFraction radians StartFraction 3 pi Over 4 EndFraction radians StartFraction 4 pi Over 3 EndFraction radians StartFraction 3 pi Over 2 EndFraction radians CAN YOU SHOW WORK PLEASE

Step-by-step explanation:

Given

Let A represent the Length of Arc CD and C, represents the circumference

Required

Find the central angle (in radians)

The length of arc CD in radians is as follows;

Where r is the radius and is the measure of central angle

The circumference of a circle is calculated as thus;

From the question, it was stated that the arc length is 2-3rd of the circumference;

This means that

Substitute for C and for A

becomes

Divide both sides by r

Hence, the measure of the central angle;

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: