Chapter 11.6, Problem 34PPS

a.

To determine

To sketch:A triangle with a base of 6 units and a height of 3 units.

Explanation of Solution

Given information:

The base of the triangle is 6 units and height of the triangle is 3 units.

Sketch:

  

Interpretation:

ABC is a triangle with base 6 units and height 3 units.

b.

To determine

To fill:Area of triangles in the table,

Answer to Problem 34PPS

Triangle	Base (in.)	Height (in.)	Area (in2)
1	6	3	9
2	12	6	36
3	18	9	81

Explanation of Solution

Given information:

The table with base and height of triangles,

Triangle	Base (in.)	Height (in.)	Area (in2)
1	6	3
2	12	6
3	18	9

Formula used: Area of a triangle is given by the formula,

  $A=\frac{1}{2}\times b\times h$

Where $A=$ area, $b=$ base, $h=$ height

Calculation:

Area of a triangle with base 6 in. and height 3 in. is given by,

  $\begin{array}{l}A=\frac{1}{2}\times b\times h\\ =\frac{1}{2}\times 6\times 3\\ =9\end{array}$

Area of a triangle with base 12 in. and height 6 in. is given by,

  $\begin{array}{l}A=\frac{1}{2}\times b\times h\\ =\frac{1}{2}\times 12\times 6\\ =36\end{array}$

Area of a triangle with base 18 in. and height 9 in. is given by,

  $\begin{array}{l}A=\frac{1}{2}\times b\times h\\ =\frac{1}{2}\times 18\times 9\\ =81\end{array}$

Thus, the table becomes,

Triangle	Base (in.)	Height (in.)	Area (in2)
1	6	3	9
2	12	6	36
3	18	9	81

c.

To determine

To explain:The effect on the area of a triangle if the dimensions are doubled and if the dimensions are tripled.

Answer to Problem 34PPS

If the dimensions are doubled the area of the triangle becomes 4 times the original area and if the dimensions are tripled the area of the triangle becomes 9 times the original area.

Explanation of Solution

Let the base of a triangle be b and the height be h .

Then, area of the triangle is given by,

  $A=\frac{1}{2}bh$

Case 1:The dimensions of the triangle are doubled.

Then the base becomes 2b and the height becomes 2h .

Then the area of the new triangle $=\frac{1}{2}\times 2b\times 2h=4\times \frac{1}{2}bh=4A$

Thus, the area of the triangle is 4 times the original area of the triangle when the dimensions are doubled.

Case 2: The dimensions of the triangle are tripled.

Then the base becomes 3b and the height becomes 3h .

Then the area of the new triangle $=\frac{1}{2}\times 3b\times 3h=9\times \frac{1}{2}bh=9A$

Thus, the area of the triangle is 9 times the original area of the triangle when the dimensions are tripled.

Conclusion:

If the dimensions are doubled the area of the triangle becomes 4 times the original area and if the dimensions are tripled the area of the triangle becomes 9 times the original area.