Question

A triangle is placed in a semicircle with a radius of 3 yd, as shown below. Find the area of the shaded region.Use the value 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your answer.3 yd1ydyd?yoХ5?

Answer 1

Notice that the area of the shaded region is the area of the semicircle minus the area of the triangle.

To compute the area of the semicircle, we use the following formula:

`\begin{gathered} A_S=(1)/(2)\pi r^2\text{.} \\ \text{Where r is the radius of the semicircle.} \end{gathered}`

Substituting r=3yd and π=3.14 we get:

`A_S=(1)/(2)(3.14)(3yd)^2=1.57\cdot9yd^2=14.13yd^2\text{.}`

Now, notice that the base of the triangle is the diameter of the semicircle, and its height is the radius, using the formula for the area of a triangle we get that:

`A_T=(b\cdot h)/(2)=((2\cdot3yd)(3yd))/(2)=9yd^2\text{.}`

Finally, the area of the shaded region is:

`A=A_S-A_T=14.13yd^2-9yd^2=5.13yd^2.`

Answer:

`5.13yd^2\text{.}`