Can someone please help me solve these problems?

[incorperated]

Directions: Find the area of each figure given the coordinates of the vertices

1.ABC with A(2,-3),B(-5,-3)and C(-1,3)

2. trapezoid FGHI with F(-1,8),G(5,8),H(3,4),and J(1,4)

3.rhomas LMPQ with L(-4,3),M(-2,4),P(0,3), and Q(-2,2)

PLease help i would very much appreciate it.

[C M Kern]

For problems 2 and 3, treat the trapezoid and rhombus as two triangles.

[C M Kern]

For the first problem:
Triangles are fascinating mathematical topics. Many other mathematical topics typically encounter or utilize elemements discovered within triangles.

Let us explore some aspects of triangles in an interactive fashion. This site will take you through some historical explorations, some interactive activities, as well as some intriguiging connections in mathematics.

A triangle in typical plane geometry is descibed as a three-sided figure or polygon whose interior angle sum is equal to 180 degrees.

The perimeter of a triangle is the sum of all three of the sides

1. Experiment with this file.

The area of a triangle is quite interesting. Often it will be represented by

Area=(1/2) x Base x Height. Where the height is an altitude drawn from the base to the opposite angle. This formula makes for a relatively easy calculation of the area of a triangle but it is rather difficult to naturally find a triangle that is given in terms of at least one side (the base) and a height. We typically can determine or are given the sides of a triangle when a triangle is present. A formula does exist that can calculate the area of a triangle when all three sides are known.

This formula is attributed to Heron of Alexandria but can be traced back to Archimedes.

This formula is represented by

Area=SQRT(s(s-a)(s-b)(s-c)),

where s=(a+b+c)/2 or perimeter/2.

[George Stearns]

Question 1 is a triangle with the first and second points having identical y values so the base has a length of abs(2-(-5)) which is 7, the height is abs(3-(-3)) or 6. The formula for the area of a triangle is 1/2 Base*Height or 1/2(7*6) or 3*7 which is 21.
A generalized way to find the area of any polygon is to draw a rectangle using the highest, lowest, most negative and most positive points and then use the area - all the triangles or rectangles on the outside.
Problem 2 is a square with 2 identical triangles outside the shape. Problem 3 if you follow the above procedure and connect the two opposite sides you will see that you have four rectangles made up of identical triangles.