Answer:
A Δ DOC = 6 in²
Step-by-step explanation:
Look at the attached graph
∵ ABCD is a trapezoid with legs AB and CD
∴ AD // BC
In Δs ABC and DCB
∵ BC is a common base
→ The heights of the Δs drawn from the points A and D to the base
BC are equal because the line joining A and D, AD is parallel to
the base BC
∴ Their heights are equal
→ Triangles of the same base and equal heights are equal in areas
∴ A Δ ABC = A Δ DCB
∵ A Δ ABC = A Δ ABO + A Δ BOC
∵ A Δ DCB = A Δ DOC + A Δ COB
→ Equate their right sides
∴ A Δ ABO + A Δ BOC = A Δ DOC + A Δ COB
∵ A Δ BOC = A Δ COB ⇒ common triangle
∴ A Δ ABO = A Δ DOC
∵ A Δ ABO = 6 in²
∴ A Δ DOC = 6 in²
