  Lesson 3ª CALCULATING THE AREA OF A SQUARE

We will base this in what we studied for rectangles. A square has 4 equal sides, which means that its height and width are the same: To calculate the area of the square, we have to multiply its length by its width. However, since they are equal, I multiply one of these measurements by itself: Test:
If you count the square centimetres, you will find 25: 15(2).10  What is the measurement of a wall whose measurements are 2 metres long by 2 metres high?

Answer: CALCULATING THE AREA OF A TRIANGLE

We will pay close attention to the rectangle to learn how to calculate the area of a triangle. In the following image, we have a rectangle that measures 10 cm. long by 8 cm. wide. Keep the diagonal in sight: 15(2).11   Draw the previous shape on a piece of paper using the same measurements and trace the diagonal line. Cut the shape and keep it safe; we will use it later on.

Look at the following shape: We have used the scissors and cut the diagonal line leaving us with two equal triangles.
Do this yourself, cut the diagonal line and you will get two identical triangles which measure 10 cm. long by 8 cm. high. But, before you cut the diagonal, what was the area of the rectangle?

Exactly: Since the rectangle has been divided into two equal parts, each one will have a value of: Each one of the two parts is a triangle whose surface equals to To get this quantity, we have multiplied the base times the height of the rectangle. Then, we have divided the result by two, since both triangles together equal the area of the rectangle.

Take a close look at the pieces you've obtained by cutting the rectangle through its diagonal. You have two triangular surfaces which, when put back together, form the rectangle once again. 15(2).12   In the previous image, you have a drawing that represents the front face of a house which needs to be painted. This geometrical shape is composed by a triangle and a rectangle. Their measurements are shown in the image.

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