Stumped by DDs YR 5 maths homework!

[trebleclef101]

Helping DD (9) with her maths homework. She is in year 5. I'm stumped by the last question (c)!

I understood it to mean draw 2 more shapes that each have the same area as perimeter (but not specifically 16cm). Then failed to come up with any simple shapes that fit the requirements.

The grid was made up of 1cm squares.

Have we misunderstood the question? Feel like I'm missing something obvious!

Invested but can’t help - please come back and say what the answer is when the homework is reviewed or marked.

Apparently you're looking for an equable shape. Apparently a 5, 12, 13 right angle triangle AND a circle with radius 2 work.

It's insane if this is what the teacher intended.

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Area & parameter both 32

I think it's quite straightforward?

1 and 2 are easy.

3 wants her to think of shape sizes that have the same area and perimeter.
They've given 4cm square as an example.
It's called an Equable Shape.

A 6 x 3 rectangle works.

She needs to find one more. 😊

A rhombus. To look at it another way, a square is a rhombus with 4 90° angles. A rhombus is a diamond. All sides the same, as long the total internal angles add up to 360°, it’s all golden!!!

It’s going to reduce the area though. If you take a square and squish it into an almost flat rhombus then the area would become almost nothing too.

@trebleclef101 have they not just made you confused by putting in a "sq with a side of 4cms"? IF They had left out the side length and just said a square with a perimeter of 16 then your could have a rectangle of 2 x 8 or 1 x 16. the area and the perimeter are still 16. and they have not said different shapes, they have just said shapes!

We've gone with a 3 x 6 rectangle and a 6 x 3 rectangle (rotated shapes will be accepted from previous experience).

Seems obvious now but needed help to get there. Maybe it's just been a long day!

But the perimeter of a 2 x 8 rectangle is 20 (8 + 8 + 2 + 2) not 16.

3 x 6 works.

@trebleclef101 We've gone with a 3 x 6 rectangle and a 6 x 3 rectangle (rotated shapes will be accepted from previous experience). the area is wrong. meant to be 16sq cms. 3 x 6 is 18 sq cms

It's supposed to be 18. Both the perimeter and area are 18.

@trebleclef101 jeezus! i am really confused now. why are you looking for 18 though

All the suggestions of circles, triangles and rhombuses are correct but beyond what the average y5 will have been taught at this point. They will however have been taught area and perimeter of rectangles (there’s only 2 possible including the square in the example) and irregular shapes (it’s literally just counting when on squared paper). The example someone hand drew above is exactly what the teacher will be looking for.

I have done this exact activity with y5 (in a lesson not as a homework) and that’s what I was looking for and what they naturally came up with.

We are looking for a shape whose area is the same as it's perimeter. That number can be anything but it needs to be the same.

A 3 x 6 rectangle has an area of 18 and a perimeter of 18 so it meets the criteria.

This isn’t true. The formula for working out the area of a parallelogram (which a rhombus is) is the same as the one for a rectangle. All the changes is the angles. Area and perimeter stay the same.

Surely it would be the height x the base to get the area of a rhombus/parrellagram rather than the product of the length of the sides.

So if you take a 5cm by 5cm square then the area is 25cm squared. But if you squish it until it’s a rhombus that’s only 4cm high (as measured by making a right angle with the bottom 5cm side up to the top corner) then the area would now be 20cm squared. The perimeter wouldn’t change though.

Yes actually you’re right. Sorry I don’t know what’s wrong with me - the only excuse I have is baby brain 🤦‍♀️😂 I just drew out what I was thinking of and in order to maintain the area the sides end up being different lengths making it no longer a rhombus. I was talking complete nonsense before 😳