Question

Calculate the area of a parallelogram with corners in (-2,-1), (-12,-4), (9,-4), (-1,-7)?

Answer 1

Area `=63" "`square units

Explanation:

From the given points

Let `A(x_a, y_a)=(-2, -1)`
Let `B(x_b, y_b)=(-12, -4)`
Let `C(x_c, y_c)=(-1, -7)`
Let `D(x_d, y_d)=(9, -4)`

The formula for polygons with points A, B, C, D is

Area `=1/2[(x_a, x_b, x_c, x_d, x_a),(y_a, y_b, y_c, y_d,y_a)]`

Area `=1/2[x_a*y_b+x_b*y_c+x_c*y_d+x_d*y_a-x_b*y_a-x_c*y_b-x_d*y_c-x_a*y_d]`

Let use the formula

Area `=1/2[(-2, -12, -1, 9, -2),(-1, -4, -7, -4, -1)]`

Area `=1/2[(-2)(-4)+(-12)(-7)+(-1)(-4)+(9)(-1)-(-12)(-1)-(-1)(-4)-(9)(-7)-(-2)(-4)]`

Area `=1/2[8+84+4-9-12-4+63-8]`

Area `=1/2[159-33]`

Area `=1/2[126]`

Area `=63" "`square units

God bless....I hope the explanation is useful.