- #1
chwala
Gold Member
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- Homework Statement
- Consider the diagram below, find the area of the shaded region
- Relevant Equations
- similarity-congruency
this is another question that i saw on the internet...
Aaaaargh the last triangle...I will re do the working again...and at same time appreciate any alternative way of doing this.Lnewqban said:AD should be 3.72 x 3.5.
I see 7 triangles, total area is 7 times 6 units of area: 42 units.chwala said:Aaaaargh the last triangle...I will re do the working again...and at same time appreciate any alternative way of doing this.
Interesting...I am an analytical person, these geometry shapes and checking for congruence or similarity I don't like it lolLnewqban said:I see 7 triangles, total area is 7 times 6 units of area: 42 units.
The diagonal line divides in half the shape formed by those 7 triangles: 21 units each big triangle.
Then, we remove the top triangle and investigate any symmetry among sides.
The top side measures 3 entire small-triangle sides.
In a symmetrical way, two of each truncated sides have the same dimension.
What could we do with that information?
Could we divide the area of the top big angle in two in order to obtain the value of the green area?
Those are only two of the ways to reach the same conclusion.chwala said:Interesting...I am an analytical person, these geometry shapes and checking for congruence or similarity I don't like it lol
Well, that's obviously wrong, or I read you wrong. Each of your two 'big triangles' is already 18 units. The green area encompasses a portion of that : looks like less than half.Lnewqban said:Therefore, the area of the green-colored parts is 6 units x 3 triangles = 18 units.
I don't mean to judge. But surely you can take 5 min out of your day to understand the definition of similar triangles, there properties, and later similarity between different geometric objects? It will save you a lot of time this route, you learn more math, and spend less time using computations you don't need to do.chwala said:Interesting...I am an analytical person, these geometry shapes and checking for congruence or similarity I don't like it lol
chwala said:Interesting...I am an analytical person, these geometry shapes and checking for congruence or similarity I don't like it lol
MidgetDwarf said:I don't mean to judge. But surely you can take 5 min out of your day to understand the definition of similar triangles, there properties, and later similarity between different geometric objects? It will save you a lot of time this route, you learn more math, and spend less time using computations you don't need to do.
It was wrong, indeed.hmmm27 said:Well, that's obviously wrong, or I read you wrong. Each of your two 'big triangles' is already 18 units. The green area encompasses a portion of that : looks like less than half.
(Not that I have anything positive to add).
Would you provide some hints on what you did? I cannot get anywhere without resorting to analytic geometry.Lnewqban said:After calculating the areas of different triangles, and using ratios among similar triangles, I have this new result:
The area of the green-colored parts is 4.5 + 2.0 + 0.5 = 7.0 units square.
I used the similar triangles idea mentioned by @MidgetDwarf in post #12 above.caz said:Would you provide some hints on what you did? I cannot get anywhere without resorting to analytic geometry.
I don't know what you mean by ASF and LSF.chwala said:MY understanding is that
But once you have those, it is obvious that the answer ischwala said:linear scale dimensions for the 1st, 2nd and 3rd triangles respectively...
While it is true that the green area above the diagonal is equal to the white area below the diagonal, there is no reasoning given to show that the green area above the diagonal equals the white area above.Zgort said:
The area is the measurement of the surface enclosed by a shape or figure.
The area of a rectangle can be found by multiplying the length by the width. The formula for area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.
The formula for finding the area of a circle is A = πr^2, where A is the area, π is the mathematical constant pi, and r is the radius of the circle.
The area of a triangle can be found by multiplying the base by the height and then dividing by 2. The formula for area of a triangle is A = (b x h) / 2, where A is the area, b is the base, and h is the height.
The process for finding the area of a shaded region depends on the shape of the region. For regular shapes like squares, rectangles, and circles, you can use the appropriate formula. For irregular shapes, you may need to break the shape into smaller, simpler shapes and find the area of each one before adding them together to get the total area of the shaded region.