Question

Find the area of shaded region ​

Answer 1

area of shaded region = 119 cm²

Explanation:

the outer figure has one pair of parallel sides and is a trapezium.

the shaded area (A) is calculated as

A = area of trapezium - area of white triangle

the area of a trapezium is calculated as

area =
`(1)/(2)` h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 14 , b₁ = 9 , b₂ = 17 , then

area =
`(1)/(2)` × 14 × (9 + 17) = 7 × 26 = 182 cm²

the area of the triangle is calculated as

area =
`(1)/(2)` bh ( b is the base and h the height )

here b = 9 and h = 14 , then

area =
`(1)/(2)` × 9 × 14 = 4.5 × 14 = 63 cm²

then area of shaded region (A) is

A = 182 - 63 = 119 cm²

Answer 2

119 cm²

Explanation:

Area of shaded region:

Area of white triangle:

base = 9 cm

height = 14 cm

`\sf \boxed{Area \ of \ triangle = (1)/(2)*base *height}`

`\sf =(1)/(2)*9*14\\\\ = 9*7\\\\= 63 \ cm^2\\`

Area of trapezium:

`\sf \boxed{Area \ of \ trapezium =((a+b)*h)/(2)}`

Here, a and b are the parallel sides of trapezium & h is the height.

a = 9 cm ; b = 17 cm and h =14 cm

`\sf Area \ of \ trapezium = ((9+17)*14)/(2)`

`= (26*14)/(2)\\\\\\=13*14\\\\= 182 \ cm^2`

Area of shaded region = area of trapezium - area of white triangle

= 182 - 63

= 119 cm²