MHB Need help on these two questions

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A high school student seeks help with two mensuration questions, providing their answers for reference. They express difficulty in calculating the height for a trapezium and verifying the area of a parallelogram split into triangles. Participants suggest showing specific problem areas for better assistance and discuss the correct application of formulas. One contributor corrects the student's initial answer for the shortest distance in a diagram, confirming it as 5.33 cm. The student expresses gratitude for the help received.
crystal_h
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Hi, I'm a high-school student and I am here for some help on these two questions on Mensuration. I have the answers, which are in the attached file below if you would like a reference. Would appreciate if u could share me your workings. Thank you! :)

1613038730726.png
 

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In terms of getting useful replies, it would probably be best if you showed us where in the two problems you are having difficulty and how we can help. If you need to refer directly to the math in either of the two problems, please be quote it directly in your post. (clicking on the .pdf link doesn't open the .pdf on my system - Ubuntu LTS 20.10).

*** edit: the image containing the two problems has been included in the OP.
 
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Beer soaked request follows.
crystal_h said:
Hi, I'm a high-school student and I am here for some help on these two questions on Mensuration. I have the answers, which are in the attached file below if you would like a reference. Would appreciate if u could share me your workings. Thank you! :)
20210211_180001.jpg

Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
 
1613112029292.png

Area of parallelogram: 10 x 8=80cm^2
As you can see I split the parallelogram into two triangles.
So, each triangle has an area of 40cm^2.
Area of triangle: 1/2 x b x h=40
Bh=20
H=20/15
=1.33
And nope, my answer's not correct.

For Question 12:
I know the formula of finding the area of the trapezium is (a+b)/2(h). The problem is, I am unable to find h. As I thought, h could be found by using Pythagoras' theorem. But I have another problem.
1613111605963.png

Please help me! Thank you.
 
Beer soaked opinion follows.
crystal_h said:
View attachment 10976
Area of parallelogram: 10 x 8=80cm^2
As you can see I split the parallelogram into two triangles.
So, each triangle has an area of 40cm^2.
Area of triangle: 1/2 x b x h=40
Bh=20
H=20/15
=1.33
And nope, my answer's not correct.
Unless I've had one too many, I'd say an accurate diagram for Question 11 lies below and the shortest distance from A to DB is more likely to be 10*sin(arcsin(8/15))=5.333... as opposed to the 5.5 cm answer that you quoted. I could of course be wrong. At any rate, someone should come along shortly to agree or disagree with my beer inspired reckoning.
20210212_211244.jpg
 
your sketch of parallelogram ABCD is incorrect ... should look like this

186F8599-7125-42BA-8CBB-999C25E08253.png
 
jonah said:
Beer soaked opinion follows.

Unless I've had one too many, I'd say an accurate diagram for Question 11 lies below and the shortest distance from A to DB is more likely to be 10*sin(arcsin(8/15))=5.333... as opposed to the 5.5 cm answer that you quoted. I could of course be wrong. At any rate, someone should come along shortly to agree or disagree with my beer inspired reckoning.
View attachment 10977
Just checked the answer given, it is actually 5.33! Thank you so much! This really helped me a lot. And thank you once again for your time and effort :)
 

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