Question

Find the area of pentagon formed by connecting coordinates P(1,-4),Q(3,-5),R(7,0),S(3,5),T(0,4).​

Answer 1

Answer:

u need to find coordinates of mid point of the pentagon, u can do it by just finding mid point of one of the diagonals and later dovide pentagon into 5 triangles and find area of each one of them and add up

Answer 2

The area of pentagon formed by connecting coordinates P(1,-4),Q(3,-5),R(7,0),S(3,5),T(0,4) is 42.5 square units.

Area of the triangle is given by = (1/2) [x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]

Area of pentagon PQRST = Area of triangle PQR + Area of triangle PSR + Area of triangle PST

For the triangle PQR, P(1,-4) Q(3,-5) R(7,0).

x₁ = 1

y₁ = -4

x₂ = 3

y₂ = -5

x₃ = 7

y₃ = 0

Putting the values, we get the area of PQR as

= (1/2) [1(-5-0) +3(0+4) +7(-4+5)]

= 7

For the triangle PRS, P(1,-4) R(7,0) S(3,5)

x₁ = 1

y₁ = -4

x₂ = 7

y₂ = 0

x₃ = 3

y₃ = 5

Putting the values, we get the area of PQR as

= (1/2) [1(0-5) +7(5+4) +3(-4-0)]

= 23

For the triangle PST, P(1,-4) S(3,5) T(0,4)

x₁ = 1

y₁ = -4

x₂ = 3

y₂ = 5

x₃ = 0

y₃ = 4

Putting the values, we get the area of PQR as

= (1/2) [1(5-4) + 3(4+4) +0(-4-5)]

= 12.5

Thus total area = 7 + 23 + 12.5 = 42.5 square units.