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find the area of the trapezoid by composing into

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Tags: Mathematik

RASTA aktiv_icon

15:42 Uhr, 13.05.2022

Tag!
dear tutors and supporters:
I am attaching the problemm.

I draw a line and I can see I have a rectangle and a triangle now.
is this a good way to find the area of this trapezoid?
Danke im Voraus.

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RASTA aktiv_icon

16:00 Uhr, 13.05.2022

I am going to post some work here and see if it is good
I am gonna find the area of the triangle first.
I have two sides
the hypotenuse and a side
hypothenuse=

10

a = 7

b =

c^{2} = a^{2} + b^{2}

10^{2} = 7^{2} + b^{2}

100 = 49 + b^{2}

100 - 49 = 49 - 49 + b^{2}

51 = b^{2}

√51=√b

b = 7.14

this is the area of the triangle
now I will find the area of the rectangle and add the two together. is this right?

Roman-22

16:22 Uhr, 13.05.2022

Decomposing the trapezoid into a rectangle and a triangle, as you did, is certainly a good way to determine the total area.
Unfortunately, the creator of the problem has made a serious mistake, because he has given too many dimensions. The side of your triangle, which you called

b,

must be

6 c m

(difference of the lengths

18 c m

and

12 c m)

. From this we can calculate the length of the hypotenuse with

\sqrt{85} c m \approx 9.22 c m

(and not

10

cm).

So depending on which of the four dimensions given you omit in your calculation you will arrive at a different total area.
I guess its best to omit the

10

cm which leads to a total area of

105 c m^{2}

ledum aktiv_icon

16:28 Uhr, 13.05.2022

The picture has a mistake
if the lower side is 12cm and the upper side 18cm the difference, your side

b

should be 6cm but your calculation with Pythagoras for

b

is also right .
having

b

the area is not

b

like you suggest but

\frac{a \cdot b}{2}

so if the 18cm are right it would be 6*7cm^2 and then the rectangle with Pythagoras you find 7*7,14cm^2
so either the 18cm or the

10

cm are wrong,
calculating with the formula for trapezoids you get the area with b=6cm
ledum

RASTA aktiv_icon

16:51 Uhr, 13.05.2022

but I thought the hypothenuse side

c

=10cm. why is it not the hypothenuse? I'm in doubt here.

Roman-22

17:05 Uhr, 13.05.2022

The side you call

c

IS the hypotenuse, but if you rely on the given measures

18 c m, 7 c m

and

12 c m,

its length can't be

10 c m

.
So EITHER of the four given length

7 c m, 10 c m, 12 c m

18 c m

must be omitted and it seems that its best to omit the

10

cm.

N8eule

17:17 Uhr, 13.05.2022

Verständigungs-Stütze:

RASTA aktiv_icon

17:22 Uhr, 13.05.2022

I get it now. I solved for

c

and got

9.22

cm like you.

okay, now

i

have

c = 9.22

a = 7

b = 6

cm

I am adding all this up to find the area

9.22 + 7 + 6

Area of the triangle

= 22.22

cm^2

area of the rectangle

A = L \cdot W

= 7 \cdot 12

= 84

cm^2

now,

22.22 + 84

(cm^2)

Area of the whole trapezoid

= 106.22

cm^2

is this correct?

thanks ledum as well. If I Did not reply directly to you was becasue your comment was similar to Roman

Roman-22

17:25 Uhr, 13.05.2022

>

Area of the triangle

= 22.22

cm^2
No!
Forget about the side

c!

You don't need it. Look at the sketch I attached at the end of my last post.
Since you have given both cathets, you can simply calculate the area with

\frac{6 c m \cdot 7 c m}{2} = 21 c m^{2}

BTW, another way to get the total area of the trapezoid would be to duplicate the whole trapezoid and compose a rectangle from the two pieces with the side lenghts 7 cm and