Question

Plot C(l, −3), D(5, −6), E(5, 4) and F(1, 1) on a graph paper. What kind of quadrilateral is CDEF? Find its area and perimeter.

Answer 1

The distance between two points (x₁​,y₁​) and (x₂,y₂) is:

Distance = `sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

CD: `sqrt((5 − 1)^2 + (−6 −(−3))^2)`

= `sqrt(16 + 9)`

= `sqrt 25`

= 5

DE: `sqrt((5 − 5)^2 + (4 −(−6))^2)`

= `sqrt(0 + 100)`

= `sqrt100`

= 10

EF: `sqrt((1 − 5)^2 + (1 − 4)^2)`

= `sqrt(16 + 9)`

= `sqrt 25`

= 5

FC: `sqrt((1 − 1)^2 + (1 − (−3))^2`

= `sqrt(0 + 16)`

= `sqrt16`

= 4

Perimeter of Quadrilateral:

Perimeter = CD + DE + EF + FC

= 5 + 10 + 5 + 4

= 24

Area of Trapezium:

Area = `1/2` × (sum of parallel sides) × height

Parallel sides = CD and EF = both are 5 units

Height = horizontal distance between vertical lines

CD (x = 1) and EF (x = 5) = 1 = 4

Area = `1/2 × (5 × 5) × 4`

Area = `1/2 × 10 × 4`

Area = 20 square units