Question

Find the area of the shaded region. Round to the nearest hundredth when necessary. Area = 25 Ft

Answer 1

Area of the shaded region would be 379. 688 ft²

To determine the area, we can see that the composite shape is made up of a cube and also a semi-circle.

The formula for area of a cube is expressed as;

Area = s²

such that 's' is the length of the side of the cube

Substitute the values, we have;

Area = 25²

Area = 625 ft²

Then, for the area of the semi -circle, we have;

Area = πr²/2

Area = 3.14 × 12.5²/2

Multiply the values

Area = 490. 63/2

Area = 245. 313 ft²

Area of the shaded region would be;

= Area of cube - area of semi -circle

= 379. 688 ft²

Answer 2

We can calculate the shaded area as the difference in the area between the square and the half circle.

The side of the square is 25 ft.

The half circle has radius equal to half the length of the side: r=25/2=12.5 ft.

Then, we can write:

`\begin{gathered} A=A_(sq)-(1)/(2)A_c_{} \\ A=a^2-(1)/(2)(\pi r^2) \\ A\approx25^2-(1)/(2)\cdot3.14\cdot12.5^2 \\ A\approx625-1.57\cdot156.25 \\ A\approx625-245.31 \\ A\approx379.69 \end{gathered}`

NOTE: Asq is the area of the square and Ac is the area of the circle, multiplied by 1/2 beacuse it is half a circle we have to substract from the square.

Answer: The shaded area is 379.69 square feet.