Area problem: find the area of the shaded part (triangle)

2022-04-28 0 By

Today is Saturday, February 5, 2022. Let’s start today’s study and continue to look at the area problem.As shown in the figure on the right, given that the area of triangle ABC is 64 square centimeters, twice the area of parallelogram DEFC, find the area of the shaded part.They give you pretty little information, but they tell you that the area of a triangle, and that the area of a parallelogram is half the area of a triangle, and they don’t know anything else.The base of a triangle is unknown, the height is unknown, the base of a parallelogram is unknown, and the height is unknown.This makes us use “parallelogram area = base × height”, “triangle area = base × height ÷2” these two area formula to find a way to crack, this road is full of thorns, do not know how to start.Maybe we can figure out the area slowly by making a false calculation, assuming the corresponding base and height, but one is difficult, the other is time-consuming.Is there any other way to find the area of this shaded area?We see that the shaded part is a triangle, and the formula for the area of the triangle is useless.So is there anything that’s the same size, or can we look around and see if we can decipher more information?It turns out, if we think of DE as the base of the shaded triangle, what’s its height going to be?Yeah it’s going to have the same height as the height of the parallelogram which means that the area of this triangle is the same as the area of the blue triangle in the picture or a triangle is related to the area of the parallelogram that has the same base and the same height, and is half the area of this parallelogram.The area of the parallelogram: 64÷2=32 square cm The area of the shadow: 32÷2=16 square cmOn the calculation of the area, if we tangle in the area formula to find the area of the relevant graph, often into a dead end, at this time, might as well go to see, which contains the relationship, starting from their relationship, the use of transformation and other ways may also get the answer you need.