EXAMPLE. Suppofe a fquare in form of a parallelogram, 18 feet long, and 9.5 feet broad, what's the content? By decimals. Feet. .5 12 The fame rule holds for a rhombus or rhom. boides: fince 'tis evident from the two next fi.. gures that all parallelograms upon the fame bafes and altitude are equal. A Rhombus. A Rhomboides. 1.45 1.67 From thefe figures it will not be difficult to conceive, that the area of every triangle is the of the parallelogram that circumfcribes it; therefore the rule for obtaining the area of any triangle, is to multiply the bafe by the perpendicular altitude, and take the of that product for the area: Or if you multiply the bafe by half the perpendicular; or multiply half the bafe by the whole perpendicular; and any of thefe three ways will give the content. An equilateral Triangle. An acute Triangle. Obferve, any angle greater than a right angle is obtufe, and that which is lefs is acute. From the foregoing problem and corollaries. likewife flow the following rule for finding the area of a trapezium and all irregular polygons. To find the area of a Trapezium. I' First divide it into two triangles by a diago nal line drawn from the two most acute angles, let fall two perpendiculars upon that diagonal line from the two remaining angles; then multiply half of that diagonal by the fum of the two perpendiculars, and the product will be the area required. Or if you add the two perpendiculars together, and take half the fum and multiply it into the diagonal, that will give the content; or you may find the areas of the two triangles, and add thofe two areas together for the content. To find the content of any irregular figure, with more fides than a trapezium. Divide it into trapeziums or triangles or what elfe it will bear; fo find the different areas feverally, and add them together for the con tent. For example; give up the content of the following irregular figure." PROBLEM II. To find the area of any regular Polygon. A regular polygon hath all its fides equal, and is fuch as can be infcribed in a circle, fo that all the angular points of it may be in the periphery or circumference of that circle which conftitutes it. There are innumerable kinds, but the most common ones are these, viz. a Pentagon of 5 fides, All which or any other may be measured by the following rule: Multiply half the fum of the fides by the radius of the infcribed circle; or multiply the fum of the fides by half the radius, and either of the products is the area. EXAMPLE. Find the content of the annext hexagon in feet and inches. F. 1. C To find the area of any Circle. A circle may be conceived as made up of an infinite number of acute triangles whose bases are |