The coordinates of the vertices of a composite figure are given. Find the area of each figure. F

The coordinates of the vertices of a composite figure are...

Key Concepts

Polygon Area Calculation

Calculating the area of a polygon involves finding a measure of the space enclosed by its vertices. This is typically done either by decomposing the polygon into simpler shapes whose areas can be easily calculated or by using formulas that take into account the coordinates of the vertices of the polygon.

Shoelace Formula

The shoelace formula is a useful mathematical algorithm for finding the area of a polygon when the vertices are known in a sequential order. By multiplying coordinates in a crisscross manner and summing these products, one can quickly determine the area of the polygon without the need for additional geometric decomposition.

Coordinate Geometry

This concept involves using the coordinate plane to represent geometric figures and perform calculations such as distances, slopes, and areas. By plotting the vertices of a figure on a coordinate system, one can apply algebraic methods to compute various properties, including the area of complex shapes.

Composite Figures

Composite figures are shapes that are formed by combining two or more simpler geometric figures. Understanding composite figures allows one to break down a complicated shape into standard parts (such as rectangles, triangles, trapezoids, etc.), making it easier to compute the total area by calculating the area of each individual component and then summing them.

Transcript

00:02 Okay, so i need to find the area of this funky looking composite figure.

00:09 So i can make a straight line going across here, and if you would have done this on graph paper, you can see that it was very straight, but it goes right, this one's at negative one, and this one's at negative one with the y, so you know that this is a straight line.

00:25 Okay, and then i'm going to go a straight line here as well.

00:33 Okay, so now i have a trapezoid here, a triangle up top, and a triangle down below.

00:41 So i need to find three areas to make this composite figure.

00:47 So let's do the triangle up above.

00:51 Okay, this point right here when graphing it is 4 -1.

01:03 So we know that the base of it is 7.

01:09 We also know the height here, and remember when you're talking about the height of a triangle, it can't be this slanted height.

01:18 It has to be 90 degrees to the base.

01:22 So the height then goes from 1 to 4, so the height is 3.

01:27 Don't forget to divide by 2 because we have a triangle.

01:31 So 21 divide by 2 is 10 .5.

01:38 Now let's do the trapezoid in the middle.