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4cm | (1) | |
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9cm | (2) | (3) |
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Rectangle 1 & 2 & 3 are similar. What is the area of Rectangle 3.
To find the area of Rectangle 3, we need to determine the dimensions of the rectangle first. Since Rectangle 1 and Rectangle 2 are similar, we can find the scale factor between them and apply it to Rectangle 3.
The scale factor can be found by comparing the corresponding side lengths of Rectangle 1 and Rectangle 2.
In this case, the side length of Rectangle 1 is 4 cm, and the side length of Rectangle 2 is 9 cm.
To find the scale factor, we divide the side length of Rectangle 2 by the side length of Rectangle 1:
Scale factor = Side length of Rectangle 2 ÷ Side length of Rectangle 1
= 9 cm ÷ 4 cm
= 2.25
Now that we have the scale factor, we can apply it to find the dimensions of Rectangle 3.
The side length of Rectangle 3 can be found by multiplying the corresponding side length of Rectangle 1 by the scale factor:
Side length of Rectangle 3 = Side length of Rectangle 1 × Scale factor
= 4 cm × 2.25
= 9 cm
Now we can calculate the area of Rectangle 3.
Area of Rectangle = Length × Width
= 9 cm × 9 cm
= 81 cm²
Therefore, the area of Rectangle 3 is 81 square centimeters.