Two mensuration problems from high school

[crystal_h]

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! :)

 

[Greg]

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.

 

[jonah1]

Beer soaked request follows.

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! :)

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.

 

[crystal_h]

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.

Please help me! Thank you.

 

[jonah1]

Beer soaked opinion follows.

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.

 

[skeeter]

your sketch of parallelogram ABCD is incorrect ... should look like this

 

[jonah1]

Beer soaked ramblings follow.

View attachment 10976
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. View attachment 10974
Please help me! Thank you.

https://www.analyzemath.com/Geometry/trapezoid_solve.html

 

[crystal_h]

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 :)

 

[crystal_h]

Beer soaked ramblings follow.

https://www.analyzemath.com/Geometry/trapezoid_solve.html

Thank you!