Question

In ABCD side AB ║ side DC, seg AE ⊥ seg DC. If l (AB) = 9 cm, l (AE) = 10 cm, A(c ABCD) = 115 cm², find l (DC).

Answer 1

Hi ,

It is given that ,

AB // DC , [ pair of opposite sides are

parallel .]

Therefore ,

ABCD is a Trapezium .

I( AB ) = a = 9 cm

I( DC ) = b cm

area ( ABCD ) = 115 cm²

AE perpendicular to CD

Altitude = h = I( AE ) = 10cm

1/2[ ( a + b )h] = area ( ABCD )

1/2 [ ( 9 + b ) × 10 ] = 115 cm²

9 + b = ( 115 × 2 )/10

9 + b = 23

b = 23 - 9

b = 14 cm

Therefore ,

I( DC ) = b = 14 cm

I hope this helps you.

: )