Farsaingeachd ceithir-cheàrnaich

Farsaingeachd parailealogram

Faodaidh sinn na ceithir-cheàrnaich a leanas a sgaradh nan ceart-cheàrnaich agus nan triantain gus an fharsaingeachd aca obrachadh a-mach.

Diagram of a parallelogram and its base and height values

Dòigh 1

Farsaingeachd triantain (1) \(A = \frac{1}{2}bh\)

\[= \frac{1}{2} \times 4 \times 5\]

\[= \frac{1}{2} \times 20\]

\[= 10\,c{m^2}\]

Farsaingeachd ceart-chearnaich (2) \(A = l \times b\)

\[= 6 \times 5\]

\[= 30c{m^2}\]

Farsaingeachd triantain (3) = co-ionann ri farsaingeachd triantain (1)

\[= 10\,c{m^2}\]

\[Farsaingeachd\ iomlan\ = 10 + 30 + 10 = 50\,c{m^2}\]

Dòigh 2

A parallelogram split into two congruent triangles along the diagonal. Parallelogram is 5cm high and 10 cm long.

Dèan dà thriantan co-chòrdach dhen pharailealogram thar aon dhe na trastain.

\[Farsaingeachd\,triantain\,A = \frac{1}{2}bh\]

\[= \frac{1}{2} \times 10 \times 5\]

\[= 25{cm^2}\]

\[Farsaingeachd\,parailealogram = 2 \times 25 = 50 {cm^2}\]

Farsaingeachd iteileig

Bhon a tha loidhne-cothromachaidh bheartagail aig iteileag bidh an aon fharsaingeachd aig triantan 1 agus 2. Bidh an aon rud fìor mu thriantain 3 agus 4.

Diagram of a 12cm x 28cm kite split into four right-angled triangles

Frasaingeachd triantain 1 \(A = \frac{1}{2}bh\)

\[= \frac{1}{2} \times 6 \times 10\]

\[= \frac{1}{2} \times 60\]

\[= 30\,c{m^2}\]

Frasaingeachd triantain 2 \(= 30\,c{m^2}\)

Frasaingeachd triantain 3 \(A = \frac{1}{2}bh\)

\[= \frac{1}{2} \times 6 \times 18\]

\[= \frac{1}{2} \times 108\]

\[= 54c{m^2}\]

Frasaingeachd triantain 4 \(= 54\,c{m^2}\)

\[Fargaingeachd\,iomlan = 30 + 30 + 54 + 54 = 168\,c{m^2}\]