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Please help. I don't get it. ​

Please help. I don't get it. ​-example-1

1 Answer

3 votes

Explanation:

what is the problem to solve ?

I assume we need to calculate the area of the whole figure ?

in any case, we have a problem :

a rhombus is a tilted square, a special parallelogram, as it has 4 equal sides.

that would mean all 4 sides of that central rhombus are 5 in.

that would make both triangles equilateral triangles (all 3 sides are equally long : 5 in).

but in order for a right-angled triangle to have the Hypotenuse = 5 in and the height (= left leg) = 4 in, that must make the right leg

5² = 4² + leg²

25 = 16 + leg²

9 = leg²

leg = 3 in

and so, the baseline of the large triangle 2×3 = 6 in.

and not 5 in, which must be the top and base line of the rhombus.

so, the whole problem definition is wrong.

the only solution when accepting the given lengths, is that the triangle sides are NOT a straight extension of the rhombus sides.

the triangle side is the Hypotenuse of the smaller internal right-angled triangle

side² = 4² + (5/2)² = 16 + 6.25 = 22.25

side = 4.716990566... in

anyway, the area of each of the large triangles is

baseline×height / 2 = 5×4/2 = 10 in²

we have 2 triangles = 2×10 = 20 in²

the area of the rhombus is

baseline×height = 5×4 = 20 in²

please note that the area of a rhombus is also

diagonal1 × diagonal2 / 2

but that applies only, when we have the lengths of the diagonals. both approaches give the same result, of course.

so, the whole area is

20 + 20 = 40 in²

User Levif
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