Problem 2. To find the Area of a Parallelogram, or Oblong Square. Def. A Parallelogram hath four Right Angles; and its oppofite Sides equal and parallel. Rule. * Multiply the Length by the Breadth, and the Product gives the Area. Example. Let ABCD be a Parallelogram, whose Length A B is 25.5 Inches, and its Breadth BD 12.75 Inches; what is the Area? Operation. 25.5 × 12.75 = 325.125, the Area in Inches. * The Reason of this Rule appears from the ist Figure, because this is only a long Square. Problem 3. To find the Area of a Rhombus. Def. A Rhombus hath four Sides all equal, but no Right Angle; it is in Shape like a Diamond Pane of Glass. Rule. * Multiply the Base by the Perpendicular Height, and the Product is the Area. Example. Let ABCD be a Quarry of Glass, or Marble; and suppose the Bafe DC be 12.5 Inches; and the Perpendicular AE 9.25 Inches; what is the Area? Operation. 12.5 × 9.25 = 115.625 Inches; the Area required. * Every Rhombus is equal to a Parallelogram of the fame Bafe and Altitude, Problem 4. To find the Area of a Rhomboides. Def. A Rhomboides hath its two Sides equal and parallel, but no Right Angle. It is a long Square pushed afide. Rule. * Multiply the longer Side by the Perpendicular Height (or Breadth), and the Product is the Area. Example. Let ABCD be a Rhomboides, whose longer Side A B, or CD, is 20.5 Inches, and the Breadth A O equal to 13-5 Inches, what is the Area? Operation. 20.5 × 13.5 = 276.75, the Area required. * Every Rhomboides is equal to a Parallelogram of the fame Bafe and Altitude. Problem 5. To find the Area of a Triangle. Def. A Triangle is a Figure bounded by three Right Lines. Note. If a Triangle hath one of its Angles a true Square, or just 90 Degrees, it is called a Right Angled Triangle; if it hath no Right Angle, it is called an Oblique Triangle. To Meafure a Right Angled Triangle. Rule. * Multiply one of the Legs forming the Right Angle by Half the other; and the Product is the Area. Example. Let ABC be a Right Angled Triangle, whose Base A B is 14.1 Inches, and the Perpendicular BC is 12 Inches; what is the Area ? Operation. 14.1 x 6 = 84.6 Inches, the Area. * Every Right Angled Triangle is equal to Half the Parallelogram of the fame Base and Altitude. Problem 6. To find the Area of an Oblique Triangle. 1 Def. If a Triangle hath no Right Angle, it is called an Oblique Triangle. Rule. * Multiply the longest Side by Half the Perpendicular let fall from the Angle oppofite the fame, and the Product is the Content. Example. Suppose ABC be a Triangle, whose Base A C is 38.6 Inches, and the Perpendicular Height BD is 30.2 Inches what is the Area? B D Operation. 38.6 × 15.1 582.86 Inches, the Area. * The Reason is because every oblique Triangle is equal to Half its Circumfcribing Parallelogram, as in the last Problem. |