Later, with the in-depth study, we gradually learned the area of combined graphics. According to the graph, we divide the combined graph, transform the irregular graph into the familiar triangle, parallelogram and trapezoid, and then add or subtract their areas to find the area of the specified graph. What we are going to talk about today is one of these situations, which requires the area of the shadow.
Example 1: Shadow A and Shadow B in the figure below are two triangles in a trapezoid, and their areas (? )
A, A is big, B is big, B is big, and C is the same size.
Analysis: If we simply analyze the areas of A and B, we will fall into a dead end. Look again, if the following c is added to both triangles, as shown in the figure:
Then figure (A+C) and figure (B+C) have the property of "the same base and the same height", so the areas of (A+C) and (B+C) are equal, so we can know that the areas of shadow A and shadow B are also equal.
Example 2, as shown in the figure: Find the shadow area.
Analysis: Here are three data: the upper base length of trapezoid 15cm, the lower base length of trapezoid 10cm. It can also be seen that the shaded part is composed of four three solutions. Can you calculate the area of each triangle separately, and then sum up to get the total area of the shaded part? Obviously impossible.
As we know, the two formulas of triangle are "base times height and then divided by 2". The known height is 10cm. As long as the length of the base can be found, the area of the triangle can be found. Let the base length of a triangle be a, b, c and d respectively, then the area of the triangle is 5a, 5b, 5c and 5d in turn, and a+b+c+d = 15, so 5a+5b+5c+5d = 5 (a+b+c+d) = 75.
Example 3. Make two line segments in a rectangle, one is its diagonal, and the other is diagonally connected from the midpoint of its side, as shown in the figure:
The areas of the two small triangles are 2 and 4 respectively. Find the area of the shaded part.
Analysis: The area of two small triangles is given separately, which is a confusing condition in itself. Now put them together, we can know that the area of the big triangle is 6. According to the area formula of triangle "base multiplied by height and then divided by 2", we can know that (length of rectangle ÷2)× width of rectangle = 12, we can calculate that the area of rectangle is 24, and the diagonal divides the rectangle into two parts, so the area of each part is 12, and then we can calculate the area of shadow part as12.
Exercise: Find the shaded area as shown in the figure.