Mathematics
Use the information given in the following figure to show that ar.(ABCQ) = ar.(ABCDE).
[Given : l // m and p // n]
Theorems on Area
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Answer
Given: l // m and p // n
To prove: ar.(ABCQ) = ar.(ABCDE)
Proof: As we know, if two triangles have the same base and height, their areas are equal.
Since AD is the common base, we have:
Area (Δ AED) = Area (Δ ADQ) ……………….(1)
Adding ar.(quad. ABCD) on both sides, we get:
⇒ ar.(Δ AED) + ar.(quad. ABCD) = ar.(Δ ADQ) + ar.(quad. ABCD)
⇒ ar.(ABCDE) = ar.(ABCQ)
Hence, ar.(ABCQ) = ar.(ABCDE).
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