Rectangle-Square Area Ratio: Find Area When Square = 16 cm²

Question

The rectangle ABCD is divided into the rectangle KBCM and the square AKMD.

The ratio between the rectangle and the square is 2:1.

The area of square AKMD is 16 cm².

Calculate the area of rectangle KBCM.

AAABBBCCCDDDKKKMMMS=18

Video Solution

Solution Steps

00:18 Let's calculate the area of rectangle K, B, C, M. Ready?
00:24 The ratio of the areas is given. Let's use this data step by step.
00:32 Now, substitute the given values in place. Let's solve for the area!
00:44 To get rid of fractions, multiply every part by 18. You're doing great!
00:50 And that's how we find the solution. Well done!

Step-by-Step Solution

First we will divide the area of KBCM by the area of AKMD.

We know that their ratio is 2:1, therefore:

KBCMAKMD=21 \frac{KBCM}{AKMD}=\frac{2}{1}

We also know the area of AKMD, so we'll substitute it into the formula to obtain the following:

KBCM18=21 \frac{KBCM}{18}=\frac{2}{1}

Finally, we multiply by 18:

KBCM=2×18=36 KBCM=2\times18=36

Answer

32

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Question Types

Area of a Rectangle: Using ratios for calculation