The best shape for your lawn is determined by its use, the landscape, appearance, and your desired maintenance level.

Design for Your Needs
The most important factor in determining the best shape for your lawn is the way you plan to use it. If the lawn will be for recreation and entertaining, it should have a large, open area, such as that provided by circular and rectangular shapes. Most lawn sports, such as croquet, badminton, volleyball, putting, and boccie ball, also require an open space; most need a playing area.

The landscape also plays a role in the shape of the lawn. Some of the most interesting lawn designs trace the shadow patterns of the house and trees during the growing season. Although some types of grass tolerate shade, most require at least six hours of sun a day. In boggy or rocky areas or those with shallow roots from nearby trees and shrubs, the soil and terrain can be modified to handle turf, or the lawn should be located elsewhere.

If your primary concern is appearance, the site itself will present the primary limiting factors. You might choose a geometric shape to project a strong sense of order, control, and formality. Open or free-flowing shapes are more playful, relaxed, and natural.

Considerations when estimating maintenance are the total number square feet to mow and the total number of linear feet to edge. Undulating lines increase the amount of edging and trimming that is required.

Four Basic Shapes

Circular The most formal lawn shape, a circular lawn makes a strong visual statement. Level circular lawns are well-suited to entertaining. When laying out a circular lawn, it is worth taking the time to get the circles perfect. If this style appeals to you, you might also like ovals and half circles.
Rectangular Rectangular lawns lend themselves best to recreation. A rectangular lawn can be seen in one glance. This lawn shape is more suited to a formal than a natural garden. Ease of maintenance makes rectangular shapes an attractive choice. Different mowing patterns add a creative touch.
Open The open lawn is the most relaxed shape. Gently flowing lines have a soothing effect on the eye and the mind and fit well with an informal garden. This type of lawn often results when you allow the shade patterns of trees to determine the shape of the lawn. Open-shape lawns are suitable for recreation and entertaining.
Free-Flowing Free-flowing lawns are ideal for creating pocket gardens. This free-flowing lawn provides five different garden areas. This shape has the added benefit of illusion; not allowing the eye to see all the lawn at once draws a person into the garden, adds mystery, and may make the garden appear larger. Be aware of how much edging is required with this shape.

Lawn design tips

	A Formal Approach This spectacular yard gains a measure of elegance from a well-tended panel of grass. The mostly symmetrical design lends a sense of formality that is in keeping with the traditionally styled house. Stone edging and paths set the lawn off in sharp relief and make mowing a snap.
	A Sense of Mystery This open lawn incorporates a sweeping curve at the far end, which serves to mask a small section of the yard. The result? The viewer assumes that the lawn continues much farther than it really does.
	Patio Extender Patios and decks are great for entertaining, but aren't always large enough to host a crowd. Here, a patch of level lawn expands the outdoor living area created by a ground-level patio. This principle would also work with a low deck that allows easy access to the lawn.
	Lawn as Pathway A narrow aisle of grass makes a very comfortable path through a landscape. Here, the path forks at the far end to create a sense of adventure for those enjoying a tour of shrubs and flowerbeds.
	Islands in the Lawn It's no crime to break up a section of lawn with a freestanding bed. Just keep in mind a few simple principles. First, make your island bed large enough to be interesting, but not so large as to overwhelm the lawn. Second, leave enough room around the island to facilitate mowing. Finally, edge the bed to keep a distinct line between bed and lawn.
	Draw the Eye Gentle curves in the edge of a lawn can direct the eye to particular features. Here, the sweep of edging on both sides of the lawn draws attention to the small grotto at the back of the yard. Well-placed curves can also draw attention away from less attractive views of neighboring homes on either side of a small plot.
	A Beautiful Frame A panel of grass is similar to the matting around a photo. That is, the flat, textureless lawn sets off the more interesting and detailed areas adjacent to it. Here, a well-cared-for lawn sets off the plantings that ring the yard. The uniform green of the lawn also helps create contrast with the darker and lighter greens of the shrub and flower foliage.
	The Pleasure Principle 1 Although it must sometimes play a subservient role in the landscape, a beautiful lawn can also be enjoyed for itself. When planning a lawn, consider the view of from various places inside your home. Viewing an expanse of grass can help soothe the senses.
	The Pleasure Principle 2 You should also create opportunities to enjoy your lawn close-up. Position a bench in a shady spot where you can gaze out upon the grass. You'll soon discover a tapestry of subtle detail that changes with the shifting breeze and the dance of sun dapples.

Source: www.bhg.com