Question

the parellel sides of a trapezium are 50 cm and 80 cm and it's non parallel sides are 26 cm and 28 cm. find the area of the trapezium.

Answer 1

Hello,
let's consider the figure.
we have that:
AB=50 cm,DF=80 cm,AD=BC=26 cm,BF=28 cm
we calculate the segment CF:
CF=DF-AB=80-50=30 cm

For Δ BCF,
we calculate the semiperimeter of triangle:p=(BC+CF+BF):2=(26+30+28):2=84:2=42 cm
we calcuate the area of triangle by Heron's formula:
AΔ=√p×(p-BC)×(p-CF)×(p-BF)=√42×(42-26)×(42-30)×(42-28)=      =√42×16×12×14=√112896=336 cm²

we calculate the height of the triangle, which is also the height of the trapezium:
BE=2AΔ:CF=(2×336):30=672:30=22.4 cm

We calculate the area of trapezium:
A=[(AB+DF)×BE]:2=[(50+80)×22.4]:2=(130×22.4):2=2912:2=1456 cm²

bye :-)

Answer 2

Step-by-step explanation:

what is the hero's fornmula