The vertices of a composite figure are given. Find the area of each figure. P(-8,7), Q(3,7), R(3

step 1 Alright, so here is our composite figure we need to find the area of. Now there are many ways yo

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

Key Concepts

Polygon Area Calculation

Polygon area calculation involves determining the total area enclosed by a multi-sided figure. When the vertices of a polygon are provided in a coordinate system, various techniques, including the shoelace formula, can be applied to compute the area without the need for traditional geometric decomposition.

Coordinate Geometry

Coordinate geometry, or analytic geometry, uses a coordinate system to represent geometric figures algebraically. It facilitates the calculation of distances, slopes, and areas by enabling the application of algebraic formulas to points defined by their coordinates.

Shoelace Formula

The shoelace formula is an efficient method for calculating the area of a simple polygon when its vertices are known in sequence. It works by summing the cross-products of coordinates in a specific order, which simplifies the computation of the area in coordinate geometry.

Composite Figures

Composite figures are shapes that consist of two or more simple geometric figures combined together. Analyzing composite figures involves recognizing the individual components that form the larger shape, which is essential for efficiently calculating properties like area.

Decomposition of Shapes

Decomposition involves breaking a complex figure into simpler, more manageable parts such as triangles, rectangles, or other basic shapes. This method simplifies the process of calculating areas, perimeters, or other properties by allowing you to compute measurements for each part and then combine the results.

Transcript

00:01 Alright, so here is our composite figure we need to find the area of.

00:06 Now there are many ways you can cut and do this.

00:10 I found three different ways.

00:13 And different ways is always great because you can try one, and then you can try another and check yourself with it.

00:20 Because if you got the same answer, then that's a good sign.

00:24 So this is the way i did it, is i created a huge, rectangle that comprised of all of the points.

00:42 And then what i'm going to do is, let me just put it down here.

00:47 Then what i'm going to do is take this large rectangle and then find this triangle here, this trapezoid here, and this triangle here, and subtract them from the large triangle that i found.

01:01 Because those shapes are not included in this shape right here that i am trying to find the area of.

01:09 So first thing again is i found the area of the rectangle.

01:15 I always want to write down rectangle.

01:17 Okay, so i know that this outer line is at negative 7, i mean negative 11, my goodness.

01:25 And this side is at 3.

01:30 So that width of that large triangle is 11 plus 3, 14.

01:41 The height goes from 7 to negative 2, so the height is 9.

01:47 So let's find that first by multiplying those two together.

01:56 Okay, now let's find the areas that i'm going to subtract because it's not included.

02:02 I'm going to find this triangle over here.

02:06 This base here, well this point right there was negative 8.

02:10 And remember our outer point is negative 11.