Chapter 1.6, Problem 21PPS

To determine

To find perimeter and area of figure

Answer to Problem 21PPS

  Area is $3.08$ meters² and perimeter is $7.8$ meters

Explanation of Solution

Given information:

Perpendicular= $6.5cm$

Base= $4.5cm$

Formula used:

  Perimeter of triangle= Sum of all sides

Area of triangle= $\frac{1}{2}(base\times perpendicular)$

Calculation:

For 3^rd vertex, use Pythagoras theorem,

  Hypotenuse= $\sqrt{{(perpendicular)}^2+{(base)}^2}$

Substituting values,

  Hyp= $\sqrt{{(6.5)}^2+{(4.5)}^2}$

Solving,

  Hyp= $\sqrt{42.25+20.25}$

Hence,

  Hyp= $\sqrt{62.5}$

So, hypotenuse is 7.9 cm

Substituting values in formula,

  Perimeter= $6.5+4.5+7.9$

Solving,

  Perimeter= $18.9$

Now,

  Area= $\frac{1}{2}(base\times perpendicular)$

Substituting values,

  Area= $\frac{1}{2}(4.5\times 6.5)$

Solving,

  Area= $\frac{29.25}{2}$

Hence, area is $12.62$ meters² and perimeter is $18.9$ meters.