Posted by **PAT** on Wednesday, April 6, 2011 at 5:13am.

Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,-1), D(-3,-1) and E (-3,2)

- geometry -
**MathMate**, Wednesday, April 6, 2011 at 7:47am
If the pentagon's boundary does not cross itself, I would use the surveyor's formula:

1. lay out the coordinates in order, repeat the first at the end.

A(0,4)

B(3,2)

C(3,-1)

D(-3,-1)

E (-3,2)

A(0,4)

2. Cross multiply between each successive pair and sum.

For A and B, we get 0*2-3*4=-12

For B and C, we get 3*-1 - 3*2 = -9

Continue until the last pair.

The sum of all 5 products is twice the area. If the vertices have been named clockwise, the sum will be negative.

3. Divide the sum by 2. If the sum is negative, write down only the positive value.

For the example:

vertex sum

A -12

B -9

C -6

D -9

E -12

Sum -48

Area = 48/2=24

Check my calculations.

## Answer this Question

## Related Questions

- geometry - Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,-1...
- geometry - A pentagon ABCDE. EG drawn parallel to DA meets BA produced at G and ...
- geometry - In the diagram, ABCDE is a regular pentagon with the measure of ...
- maths - The convex pentagon ABCDE has a right angle at B,AB=BC andCD=DE=EA=1cm,...
- pentagon...GEOMETRY - ABCDE is a regular pentagon. FAD is an equilateral ...
- Math - the area of ABCDE is 18 sq. cm.; the area of a similar pentagon PQRST is ...
- Algebra Grade 7 - Pentagon ABCDE ~ Pentagon FGHIJ. Find BC for GH =12, IJ = 15 ...
- maths - ABCDE is a Pentagon with BE parallel to CD and BC parallel to DE. BC is ...
- Geometry - Find the area of a trapezoid ABCD with verticles A(2,2) B(4,6) C(4,-3...
- Multivariable Calculus - A pentagon is formed by placing an isosceles triangle ...