Question

Find the area of a trapezium of which the parallel sides are 102 and 60 m. the other two sides
are 34 and 20 m.

Answer 1

Answer:

1296m²

Step-by-step explanation:

Use the Pythagorean Theorem on each of the right triangles.

A. h2+(42−x)2=342 and B. h2+x2=202

Solve equation B for h2 : h2=400−x2

Substitute this value of h2 into equation A and expand (42−x)2 :

400−x2+1764−84x+x2=1156

Notice that the x2 cancel out, now solve for x:

2164−84x=1156

−84x=−1008

x=12m

Now find the value of h: h2=400−122=256 , h=16m

The formula for the area of a trapezium is: A=12h(b1+b2)

Substitute the values in and simplify:

A=12(16)(102+60)=8(162)=1296m²