Find the area of Fig, in the following ways: (i) Sum of the areas of t

1.	Find the area of Fig, in the following ways: (i) Sum of the areas of three triangles (ii) Area of a rectangle — sum of the areas of five triangles
Answer» (i) From the figure, P is the midpoint of AD. Thus AP = PD = 25 cm and AB = CD = 20 cm From the figure, we observed that, Area of Triangle APB = Area of Triangle PDC Area of Triangle APB = ½ (AB x AP) = ½ (20 x 25) = 250 cm² Area of Triangle PDC = Area of Triangle APB = 250 c m² Area of Triangle RPQ = ½ (Base x Height) = ½ (25 cm x 10 cm) = 125 cm² Hence, Sum of the three triangles = (250 + 250 + 125) cm² = 625 cm² (ii) From the figure, area of the rectangle ABCD = 50 cm x 20 cm = 1000 cm² Thus, Area of the rectangle – Sum of the areas of three triangles = (1000 – 625) cm² = 375 cm²

Find the area of Fig, in the following ways: (i) Sum of the areas of three triangles (ii) Area of a rectangle — sum of the areas of five triangles

Answer»

(i) From the figure, P is the midpoint of AD.

Thus AP = PD = 25 cm and AB = CD = 20 cm

From the figure, we observed that,

Area of Triangle APB = Area of Triangle PDC

Area of Triangle APB = ½ (AB x AP)

= ½ (20 x 25)

= 250 cm²

Area of Triangle PDC = Area of Triangle APB = 250 c m²

Area of Triangle RPQ = ½ (Base x Height)

= ½ (25 cm x 10 cm)

= 125 cm²

Hence, Sum of the three triangles = (250 + 250 + 125) cm²

= 625 cm²

(ii) From the figure, area of the rectangle ABCD = 50 cm x 20 cm

= 1000 cm²

Thus, Area of the rectangle – Sum of the areas of three triangles

= (1000 – 625) cm²

= 375 cm²