Question

Polygon CCC has an area of 404040 square units. K 2ennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 1 ​2 start fraction, 1, divided by, 2, end fraction and labeled it Polygon DDD. What is the area of Polygon DDD?

Answer 1

Explanation:

10

Answer 2

Area of polygon D = 10 square units

Explanation:

Given:

Polygon C has an area of 40 square units.

It is scaled with a scale factor of
`\frac{1}2` to form a new polygon D.

To find:

The area of polygon D = ?

Solution:

When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.

And the area becomes one-fourth of the original polygon.

Let us consider this by taking examples:

• First of all, let us consider a right angled triangle with sides 6, 8 and 10 units.

Area of a right angled triangle is given by:

`A = (1)/(2) * Base * Height\\\Rightarrow A = (1)/(2) * 6 * 8 = 24\ sq\ units`

If scaled with a factor
`(1)/(2)`, the sides will be 3, 4 and 5.

New area, A':

`A' =(1)/(2) * 3 * 4 = 6\ sq\ units = \frac{1}4* A`

i.e. Area becomes one fourth.

• Let us consider a rectangle now.

Sides be 8 and 10 units.

Area of a rectangle, A =
`Length * Width` = 8
`*` 10 = 80 sq units.

Now after scaling, the sides will be 4 and 5 units.

New Area, A' = 4
`*` 5 =20 sq units

So,
`\bold{A' = \frac{1}4 * A}`

Now, we can apply the same in the given question.

`\therefore` Area of polygon D =
`\bold{(1)/(4)}`
`*` Area of polygon C

Area of polygon D =
`\bold{(1)/(4)}`
`*` 40 = 10 sq units