Chapter 14.5, Problem 26PSD

To determine

To write a paragraph proof for showing the given procedure is valid.

Explanation of Solution

Given:

The procedure is given as-

1. Draw diagonal PR.
2. Construct a line parallel to PR through Q, intersecting SR at some point T.
3. Draw PT.
4. $\text{Area(VPST) = ar(quadPQRS) }$

Calculation:

Proof-

The given quadrilateral PQRS is

  

Now, the construction of the triangle having the area equal to the above quadrilateral is as follows-

  

After observing the procedure and construction both, the procedure seems correct and valid.

To determine

To construct a triangle that is equal in area to a given pentagon.

Explanation of Solution

Given:

The pentagon.

Calculation:

The triangle that is equal in area to a given pentagon can be constructed as follows-

Step 1- construct a pentagon and have the five triangles in it.

Step 2- Now find the area of one triangle of pentagon.

Step 3- multiply the area found by $\text{5}$

Step 4- Now draw a triangle ABC of area equal to the five times the area of one triangle.