Answer:
276 cm²
Step-by-step explanation:
Area of trapezium:
Construct a line DE parallel to AB.
DE = 13 cm
So, ABED is a parallelogram
In ΔDEC,
DE = a = 13 cm
EC = AB - BE
= 30 - 16
EC = b = 14 cm
DC = c = 15 cm
Use Heron's formula to find the area of triangle.
[tex]\sf s = \dfrac{a+b+c}{2}\\\\=\dfrac{13+15+14}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]
s-a = 21 - 13 = 8
s - b = 21 - 14 = 7
s - c = 21 - 15 = 6
[tex]\sf \boxed{\bf Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)} }[/tex]
[tex]\sf = \sqrt{21 * 8 * 7* 6}\\\\=\sqrt{3 * 7 * 2* 2 * 2 * 7 * 2 * 3}\\\\= 3 * 7 * 2 * 2\\\\= 84 \ cm^2[/tex]
Area of ΔDEC = 84 cm²
[tex]\sf \dfrac{1}{2}*base * height = 84\\\\ \dfrac{1}{2}*14*height = 84[/tex]
[tex]\sf height =\dfrac{84*2}{14}\\\\[/tex]
= 6 *2
height = 12 cm
Now we know the height of the trapezium. h = 12 cm
The length of the parallel sides are a = 30 cm & b =16 cm
[tex]\sf \boxed{Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]
[tex]\sf =\dfrac{(30+16)*12}{2}\\\\=\dfrac{46*12}{2}\\\\= 23 * 12\\\\= 276 \ cm^2[/tex]
