Question

In a trapezium ABCD, AB is parallel to CD. AB =30cm, BC=15cm, DC=44cm, and AD=13cm.Find the area of that trapezium??

Answer 1

Translate D by vector AB, and let its image be E. Quadrilateral ABED is a parallelogram, so EB is equal in length to DA. Now consider triangle EBC. All three sides are known. 

EB = 13 cm 
BC = 15 cm 
CE = 14 cm 

Use Heron's formula. For triangles that is. There is no Heron's formula for quadrilaterals. 

(13 + 15 + 14)/2 = 21 

area(EBC) = √[21(21 - 13)(21 - 15)(21 - 14)] 
= √[21(8)(6)(7)] 
= √(7056) 
= 84 

Let EC be the base of that triangle. Find its corresponding height. 

(base)(height)/2 = area 
14h/2 = 84 
h = 12 

The height of triangle EBC is 12 cm. That is also the height of the trapezium. 

area(ABCD) = (AB + DC)h/2 
= (30 + 44)(12)/2 
= 444 cm² 

ANSWER....

Answer 2

Translate D by vector AB, and let its image be E. Quadrilateral ABED is a parallelogram, so EB is equal in length to DA. Now consider triangle EBC. All three sides are known.  

EB = 13 cm  

BC = 15 cm  

CE = 14 cm  

Use Heron's formula. For triangles that is. There is no Heron's formula for quadrilaterals.  

(13 + 15 + 14)/2 = 21  

area(EBC) = √[21(21 - 13)(21 - 15)(21 - 14)]  

= √[21(8)(6)(7)]  

= √(7056)  

= 84  

Let EC be the base of that triangle. Find its corresponding height.  

(base)(height)/2 = area  

14h/2 = 84  

h = 12  

The height of triangle EBC is 12 cm. That is also the height of the trapezium.  

area(ABCD) = (AB + DC)h/2  

= (30 + 44)(12)/2  

= 444 cm²