Find the area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5.

To find the area bounded by

Y = 4x + 5 (Say AB) …(i)


Y = 5 – x (Say BC) (ii)


4y = x + 5 (Say AC) ...(iii)


By solving equation (i) and (ii), points of intersection is B (0, 5)


By solving equation (ii) and (iii), points of intersection is C (3, 2)


By solving equation (i) and (iii), we get points of intersection is A ( – 1, 1)


These are shown in the graph below:



Required area = area of (ΔABD) + area of (ΔBDC) …(1)


Area of (ΔABD) =







…(2)


Area of (ΔBDC) =







Area of (ΔBDC) = …(3)


Using equation (1), (2) and (3)


Required area = Area (ΔABD) + Area (ΔBDC)




Required bounded area of = Area of (ΔABD) + Area of (ΔBDC) =


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