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# Please help with this maths question...

(19 Posts)Top one is base x height divided by two

1x 0,75 |2 = 0.375

Bottom one is

3x2.25 |2 = 3.375

I think !!

Hope that helps !

The only way I can think of is to work out the areas of the large triangles and then the areas of some smaller triangles to form a square - you can work these out as each small square is 1 unit x 1 unit. Add up all the triangles and take off the area of the square.

I know what i mean but not sure that makes sense...

Hmm - thanks- but answers are apparently 1/3 and 128/35.

Can't believe I have the answers but can't work out how to get them...this is for a 10 year old...

I'll try and explain better. Draw a square around the triangles and work out the areas of the "gaps" which are either right angle triangles or squares. Add up all the "gap" shape areas and the large triangle areas and then take away the area of the square.

I think it’s similar triangles.

For the first one, the bottom is 6 and the side is 4. Because you’re cutting a right angle triangle out of that but the slope is the same angle the shaded triangle must be 6:4 and it’s 1 along the bottom so it must be 1:4/6 so the area is (1 x 4/6)/2 = 1/3

This is hard for a 10 year old!

I would solve it by using the fact that the small shaded triangle is just a smaller version of the larger one at the bottom (as hypotenuse is the same angle) So use ratios to find the height of the vertical side (6:4 = 1:?) then use half base x height to find the area.

Sorry that doesn't work..! Me and my maths degree are stuck!

Cross posted with **@DelurkingAJ**! Sorry!

Actually it would work but needs trigonometry do assume there's an easier way.

Thanks all- I am going to have a glass of wine and tackle it again tomorrow with your help. I figure there must be an easy ish way to do it given the age group...

I would do it using the gradient of the larger triangle to work out the height of the shaded triangle as **Delurking** suggests, but that doesn’t seem within the grasp of a 10 year old.

It's a mock 11 plus paper so technically for scholarship boys as well- last question on the paper so my DC unlikely to get to it anyway- But I want to be able to work it out!

Definitely similar triangles and ratio/scale factor. No, not easy and the info about where it came from makes sense - it requires some serious problem solving skills!

You can use the ratios of the base to height to work out the base and height of the shaded triangle. First question the height is 2/3 of the base, base is 1, so area is 1/3 unit. Second is more complicated.

As pp said it is similat triangles.

If you look at first example and specifically the larger triangle. This has area of 6x 4 x 0.5 or 12 cm squared.

Now the small shaded triangle has length of 1 square compared to 6 for the larger similar triangle

This means each side is 1/6th of its larger cousin. The area will be 1/6 x 1/6 or 1/36th of the larger one.

So 12/36 = 1/3.

Another way to look at it that if length of shaded is area is 1 to compared to 6 then height will be 4/6 or 2/3.

Area is therefore 1 x 2/3 x 1/2 or 1/3

Second question the bottom triangle is has base to height ratio of 7:5. Shaded triangle is the same as similar.

Height easiest to work out as it's 3 units down from the top right of the larger triangle to the base of the shaded triangle, but the shaded triangle starts one unit to the left, so the height is 3 - 5/7 = 16/7 units. Base is 7/5 of the height, so 16/5 units. 1/2 * 16/5 * 16/7 = 128/35. I'm sure someone can show it more clearly with a diagram.

Haha. My son who has a grade 8 gcse is laughing. He thinks this is insane. He cant do it, at least notin the middle of Saturday morning relaxation 😂.

He is cursing the ridicule of how irrelevant school maths in the real world. Obviously we all use these triangular calculations in every day life..I do😉 (even my sister doesnt an shes a product designer)

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