Question

in a Trapezium ABCD ab parallel DC ab = 30 cm and BC = 15 cm is equal 44 cm and 13 cm find the area of the trapezium​

Answer 1

Answer:

Explanation: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