Chapter 11.9, Problem 9PPS

To determine

To calculate the area of the figure.

Answer to Problem 9PPS

  $7.3$ square millimeters.

Explanation of Solution

Given information:

The figure is can be divided into a rectangle, triangle and semi-circle.

Rectangle has length $l=2.4$ millimeters and breadth $b=1.6$ millimeters.

Triangle has base $B=1.6$ millimeters and $H=1.5$ millimeters.

Semicircle has a diameter $d=2.4$ millimeters, thus radius $r=\frac{d}{2}$

  $=\frac{2.4}{2}$

  $=1.2$ millimeters.

Formula used: Area of rectangle $R=l\times b$

Area of triangle $T=\frac{1}{2}\times B\times H$

Area of semicircle $S=\frac{\pi \times r^2}{2}$

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

Calculation:

  $R=l\times b$

Area of the rectangle

  $=2.4\times 1.6$

Putting the values in the formula

  $=3.84$ square millimeters.

  $T=\frac{1}{2}\times B\times H$

Area of triangle

  $=\frac{1}{2}\times 1.6\times 1.5$

Putting the values in the formula

  $=0.8\times 1.5$

Simplifying the expression.

  $=1.2$ square millimeters.

  $S=\frac{\pi \times r^2}{2}$

Area of semicircle

  $=\frac{\pi \times 1.2\times 1.2}{2}$

Putting the values in the formula

  $=\frac{22}{7\times 2}\times 1.2\times 1.2$

Simplifying the expression

  $=2.26$ square millimeters.

Now, total area is the sum of the area of the three figures.

  $=R+T+S$

  $=3.84+1.2+2.26$

Adding the values

  $=7.3$ square millimeters.