Chapter 11, Problem 16PT

To determine

To calculate the area of the shaded region.

Answer to Problem 16PT

  $132.5$ squarefeet.

Explanation of Solution

Given information:

The shaded area consists of a triangle and a square. The value of 1 square are is equal to 5 square feet.

The shaded figure consists of two figures- a square and a triangle.

Let the area of the triangle be ‘t’ and that of the square be ‘s’.

In the case of the triangle, notice that is exactly half of a rectangle that covers

  $7\times 3=21$ square units.

Hence, it can be concluded that the area of the triangle would be half the area of the rectangle covering 21 square units.

Area of the triangle ‘t’.

  $=21\times 5\times \frac{1}{2}$

Since the area of 1 square unit is 5 square feet.

  $t=52.5$ square feet.

In the case of the square, the number of square units covered is

  $4\times 4=16$ square units.

Hence the area of the given square is

  $=16\times 5$

Since the area of 1 square unit is 5 square feet.

  $s=80$ square feet.

Now, the total area of the composite figure shall be $t+s$

  $=52.5+80$

Adding the respective areas.

  $=132.5$ square feet.