Hi, could you please help me to calculate the height of the trapezium in question no 4 Q - Maths - Understanding Quadrilaterals

Question

Hi, could you please help me to calculate the height of the
trapezium in question no 4

Q 4 In quadrilateral ABCD, AB=10 cm, BC= 6 cm, CD=
2 8 cm, DA = 6 cm and its diagonals are 8 cm each
(i) Are ∠ ADB and ∠ ACB right angles?
(ii) Is ABCD a trapezium? If yes, find its height
(iii) Find the area of the quadrilateral

Shruti Tyagi · Accepted Answer

Dear student,

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5aa37f7aef5db%20jpg"
style="width: 350px; height: 220px;">
Construction: Draw DE and CF perpendicular to AB
Given: CD=2
8 cm and AB=10 cmSince CD=2
8 cm ⇒EF=2 8 cmNow, AB-EF=10-2 8=7
2 cmAE=EF=7 22=3
6 cm In ∆DAEBy pythagoras theoremAD2=DE2+AE2⇒62=DE2+3
62⇒36=DE2+12 96⇒DE2=36-12 96⇒DE2=23
04⇒DE=±4
8 cm      (neglecting -ve value as length can't be -ve)Thus the height of trapezium is 4
8 cm

Regards