Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

3. Let P be a parallelogram with vertices at (0,0), (a, b), (a + c, b + d), and (c, d), oriented counter- clockwise. This

image text in transcribed
3. Let P be a parallelogram with vertices at (0,0), (a, b), (a + c, b + d), and (c, d), oriented counter- clockwise. This means that the inside of the parallelogram is to the left as you walk around the perimeter according to the order of the vertices above, see Figure 2. Prove that the area of P is ad be by cutting P into pieces and reassembling them into a rectangle, as in Figure 3. (For simplicity assume that a, b, c, d 2 0 so that the pictures below are accurate.) Also prove that the area of the triangle with vertices at (0,0), (a, b) and (c, d) is %(ad bc). (a+c,b+d) (c, d) (a, b) (0, 0) Figure 2: A parallelogram. g Figure 3: Idea for a proof of the formula for the area of a parallelogram with vertices at (0,0), ((1, b), (a | c, b + d), and (c, d), where a, b, c, d > 0. The rst, third, and fth parallelograms have the same area. The lower left vertex is at (0, 0) in all the gures. What are the sides of the nal rectangle? (c, d) ('11 b) (01 0)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Introductory Algebra

Authors: Julie Miller, ONeill, Nancy Hyde

2nd Edition

0077473418, 9780077473419

More Books

Students also viewed these Mathematics questions

Question

What reward will you give yourself when you achieve this?

Answered: 1 week ago