Question

What is the area of the smaller figure in square cm?

Answer 1

(25 + 25/√2)²

= 25² + 50*25/√2 + (25/√2)²

= 625 + 1250/√2 + 625/2

≈ 625 + 883.883 + 312.5

≈ 1821 sq. cm

Explanation:

Imagine starting by putting the diameter of the semicircle directly in the corner of a square but at a 45 degree angle. That makes a 45-45-90 triangle with the hypotenuse being 50 cm.

Now take the midpoint of this and draw your semicircle. The distance from this point up will be the radius (25 cm). And down will be the side of a triangle with hypotenuse 25. This ends up being 25/√2.

So one dimension would be 25 + 25/√2, and so would the other. Multiplying this together we get:

Answer 2

The area of the smaller rectangle is 8 cm²

EXPLANATION

Let the area of the smaller rectangle be s.

The scale factor for the enlargement is

`k = 5`

The corresponding change is area is

`{k}^(2) = {5}^(2) = 25`

When we multiply this by the area of the smaller rectangle we obtain the area of the bigger rectangle.

`25s = 200`

`s = (200)/(25)`

`s = 8 {cm}^(2)`