Question

Find the missing values.

S. No.	Height 'h'	Parallel side 'a'	Parallel side 'b'	Area
(i)	10 m	12 m	20 m
(ii)		13 cm	28 cm	492 sq. cm
(iii)	19 m		16 m	323 sq. m
(iv)	16 cm	15 cm		360 sq. cm

Answer 1

(i) Given Height h = 10 m; Parallel sides a = 12 m; b = 20 m 

Area of the Trapezium = \(\frac{1}{2}\)h(a + b) sq. units 

= \(\frac{1}{2}\) x 10 x (12 + 20)m² 

= (5 x 32)m² = 160 m²

(ii) Given the parallel sides a = 13 cm; 6 = 28 cm 

Area of the trapezium = 492 sq. cm 

\(\frac{1}{2}\)h(a + b) = 492 

\(\frac{1}{2}\) x h x (13 + 28) = 492 

h x 41 = 492 x 2

h = \(\frac{492\,\times\,2}{41}\)

h = 24 cm

(iii) Given height ‘h’ = 19 m; Parallel sides b = 16 m 

Area of the trapezium = 323 sq. m 

\(\frac{1}{2}\)h(a + b) = 323 

\(\frac{1}{2}\) x h x (a + 16) = 323 

a + 16 = \(\frac{323\,\times\,2}{19}\) = 34 

a = 34 – 16 = 18 m 

a = 18 m

(iv) Given the height h - 16 cm; Parallel sides a = 15 cm 

Area of the trapezium = 360 sq. cm 

\(\frac{1}{2}\) x h x (a + b) = 360 

\(\frac{1}{2}\) x 16 x (15 + 6) = 360 

15 + b = \(\frac{360}{8}\) = 45 

b = 45 – 15 = 30 

b = 30 cm

Tabulating the results we get

S. No.	Height 'h'	Parallel side 'a'	Parallel side 'b'	Area
(i)	10 m	12 m	20 m	160 m2
(ii)	24 cm	13 cm	28 cm	492 sq. cm
(iii)	19 m	18 m	16 m	323 sq. m
(iv)	16 cm	15 cm	30 cm	360 sq. cm