ABCD is a rectangle with area equal to 36 square units. Points E, F, and G are midpoints of the sides on which they are located. How many square units are there in the area of triangle EFG? Explain your answer in detail.
Try drawing it. Plot a point in the middle of three of the sides. It cuts the rectangle in half. The area that remains would be 18 square units. Now draw a line from the middle of the base of the triangle (the line cutting the rectangle in half) up to the point above it. You have now cut the remaining rectangle part into two smaller rectangles. Each of these rectangles is cut in half by a diagonal line, which is a side of the triangle. I think this would mean that the triangle is taking up half of the area that is remaining, which would be 9 square units.
A + B + C + D = 36, right? So if EFG is half of it, then you minus the corners and there you have it! The answer is 9 square units
I would just like to say that this question is very stupid and irrelevant in real life. I don’t know why that make kids do this is math class as an Olympiad question because it will not help them in real life. But since you still need the answer because simply me ranting about how stupid these math questions are will not help you in any way I will give you the answer. The answer that you are looking for is 9. Why? Because it is, just deal with it!
9 because the side is 4 by 9 and do plug and chug so triangle is A= bh* 1/2
Boi stop
To find the area of triangle EFG, we need to determine the length of its base and height. Since E, F, and G are midpoints of the sides of rectangle ABCD, we can conclude that triangle EFG is similar to triangle ABC, as both triangles have corresponding sides in the same ratio.
Let's denote the length of side AB as 'a' and the length of side BC as 'b'. Since ABCD is a rectangle, we know that AB = CD and BC = AD.
Since ABCD has an area of 36 square units, we can set up the equation:
AB * BC = 36
Substituting in the values of AB and BC, we have:
a * b = 36
Since E, F, and G are midpoints, we know that EF = FG = GE = 0.5 * AB and EG = 0.5 * BC. Therefore, the base of triangle EFG is EF + FG = 0.5 * AB + 0.5 * AB = AB, and the height is EG = 0.5 * BC.
Now that we have determined the base and height of the triangle, we can calculate the area of triangle EFG using the formula for the area of a triangle:
Area of triangle EFG = (base * height) / 2
Substituting in the base and height we found:
Area of triangle EFG = (AB * EG) / 2
= (AB * 0.5 * BC) / 2
= 0.25 * (AB * BC)
= 0.25 * 36 (since AB * BC = 36)
= 9
Therefore, the area of triangle EFG is 9 square units.