Answer:
<em>Area of polygon D = 10 square units</em>
Step-by-step explanation:
<u>Given:</u>
Polygon <em>C </em>has an area of 40 square units.
It is scaled with a scale factor of to form a new polygon D.
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<u>To find:</u>
The area of polygon D = ?
<u>Solution:</u>
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 <em>6, 8 and 10 units.</em>
Area of a right angled triangle is given by:
If scaled with a factor , the sides will be 3, 4 and 5.
New area, A':
i.e. Area becomes one fourth.
- Let us consider a rectangle now.
Sides be 8 and 10 units.
Area of a rectangle, A = = 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,
Now, we can apply the same in the given question.
Area of polygon D =
Area of polygon C
Area of polygon D = 40 = <em>10 sq units</em>