# Geometry Problem 1494 with Solution: Parallelogram, Midpoints, Octagon, Areas

The figure below shows a parallelogram ABCD with midpoints M, N, P, and Q
of its sides AB, BC, CD, and AD respectively. The lines AN, AP, BP, BQ,
CM, CQ, DM, and DN intersect to form an octagon EFGHIJKL with area S_{1}.
You are required to prove that \({S_1} = {7 \over 25}{S}\), where S is the
area of parallelogram ABCD.

View solution below

## Typography and Sketch of Problem 1494

### Geometric Art using Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.