![]() This entry was posted in Geometry and tagged area of a rectangle, area of a square, derivation of the area of a rectangle, proof of the area of a rectangle by Math Proofs. Reference: Geometryby Edwin E Moise and Floyd L. Subtracting x^2 + y^2 from both sides results toīut $latex x$ and $latex y$ are the length and width of the rectangle, therefore, the area of any rectangle is the product of its length and its width. Clearly, the area of the largest square is the sum of the areas of the two smaller squares and the two rectangles. Now, let $latex A$ be the area of each rectangle shown above. This means that the area is equal to the length of the rectangle times its width. We do not know the area of the rectangle yet because that is what we are trying to prove. The equation for finding the area of a rectangle is simply A L W. We already know that the area of the two squares are $latex x^2$ and $latex y^2$. The square is divided into four parts: two squares and two rectangles. Theorem: The area of a rectangle is the product of its length and width.Ĭonsider the square below with side length $latex x + y$ units. The area of the semi-circle is one-half the area of a circle. We show that it is the product of its length and its width. The length and width of the rectangle are 10 in and 4 in respectively, so its area is. However, how do we prove that it is indeed true? In this post, we are going to discuss the proof of the area of a rectangle. What about the area of a rectangle?īased on the finding the area of a square, our intuition tells us that it is the product of the length and the width. For example, a square with side length 5 units has area 25 square units. ![]() We can easily calculate the area of a square by squaring its side length. The unit of area of the rectangle is square units. You can find the area of a rectangle by multiplying the length times the width Learn the steps and master this third-grade skill with this quick, free lesson. In getting the areas of figures, calculating the area of a square is probably the easiest. The area of a rectangle is the product of its two sides, multiplying the length and its breadth.
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