Chapter 11.9, Problem 4CYU

To determine

To calculate the area of the given figure.

Answer to Problem 4CYU

  $100.3$ square feet.

Explanation of Solution

Given information:

Figure consists for a rectangle with length $l=5.7$ feet and breath $b=2.8$ feet.

It also consists of two equal semicircles with diameter $d=6$ feet or radius $r=\frac{6}{2}$

  $=3$ feet.

Formula used:

Area of rectangle $A=l\times b$ . Where ‘l’ is the length and ‘b’ is the breath.

Area of circle $a=\pi \times r^2$ where ‘r’ is the radius. Since both the semicircles are of equal diameter and radius.

For calculations, $\pi =\frac{22}{7}$ has been used.

Calculation: Calculate the area of the rectangle and circle. On adding the two, the area of the figure shall be derived.

  $A=l\times b$

Formula of rectangle

  $=12\times 6$

Multiply the length and breadth

  $=72$ square feet.

Next, calculate area of the circle.

  $a=\pi \times r^2$

Formula of circle

  $=\frac{22}{7}\times 3^2$

Expand the exponent of 3.

  $=\frac{22}{7}\times 9$

On simplification

  $=28.29$ square feet.

Adding the two areas would give the area of the figure.

  $=72+28.29$

  $=100.29$ square feet.

  $=100.3$ square feet, rounded to the nearest tenth.