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Area Formulas for Common Shapes: Rectangles, Parallelograms, Triangles, and More

This guide provides essential area formulas for various geometric shapes, including rectangles, parallelograms, triangles, trapezoids, kites, regular polygons, circles, and annuli. Each section includes the corresponding formula, such as A = bh for rectangles and parallelograms, A = 1/2 bh for triangles, and A = πr² for circles. Additionally, special cases like Pick's Formula for polygons with lattice points and sectors of circles are explained. Learn how to calculate the area for these shapes using base and height or diagonals, enhancing your geometry skill set.

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Area Formulas for Common Shapes: Rectangles, Parallelograms, Triangles, and More

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  1. C-75 p. 411 Chapter 8 - Area Rectangle Area Conjecture The area of a rectangle is given by the formula …. A = bh ...where A is the area, b is the length of the base, and h is the height of the rectangle. Note: You can use this formula two ways, each one using a different side as base

  2. C-76 p. 412 Chapter 8 - Area Parallelogram Area Conjecture The area of a parallelogram is given by the formula …. A = bh ...where A is the area, b is the length of the base, h is the parallelogram height. Note: You can use this formula two ways, using a different side as the base.

  3. C-77 p. 417 Chapter 8 - Area Triangle Area Conjecture The area of a triangle is given by the formula …. A = 1/2 bh ...where A is the area, b is the length of the base, and h is the height of the triangle. Note: This formula can be used three different ways, each one using a different side as the base.

  4. C-78 p. 418 Chapter 8 - Area Trapezoid Area Conjecture The area of a trapezoid is given by the formula …. A = 1/2 (b1+b2)h ...where A is the area, b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid.

  5. C-79 p. 418 Chapter 8 - Area Kite Area Conjecture The area of a kite is given by the formula …. A = 1/2 d1 d2 ...where A is the area, d1 is the length of one diagonal, d2 is the length of the other diagonal of the kite.

  6. C-80 p. 427 Chapter 8 - Area Regular Polygon Area Conjecture The area of a regular polygon is given by the formula …. A = 1/2 asn ...where A is the area, a is the length of the apothem, s is the length of a side, and n is the number of sides.

  7. C-80 p. 427 Chapter 8 - Area Regular Polygon Area Conjecture, coda The area of a regular polygon is also given by the formula …. A = 1/2 aP ...where A is the area, a is the length of the apothem, P is the perimeter. ( Note: P = sn )

  8. p. 431 Chapter 8 - Area Pick’s Formula If A is the area of a polygon whose vertices are lattice points, b is the number of lattice points on the boundary of the polygon, and i is the number of interior lattice points, then.... A =1/2 b + i -1

  9. C-81 p. 434 Chapter 8 - Area Circle Area Conjecture The area of a circle is given by the formula... A = πr2 ...where A is the area and r is the radius of the circle.

  10. Section 8-6 p. 437 Chapter 8 - Area Annulus Area Formula The area of an annulus is given by the formula... A = π(R2 -r2) ...where A is the sector area, R is the radius of the outer circle r is the radius of the inner circle.

  11. Section 8-6 p. 437 Chapter 8 - Area Sector Area Formula The area of a sector of a circle is given by the formula... A = (x/360)πr2 ...where A is the sector area, x is the number of degrees of the sector arc, and r is the radius of the circle.

  12. Section 8-6 p. 437 Chapter 8 - Area Segment Area Formula The area of a segment of a circle is given by the formula... A = (x/360)πr2– 1/2 bh ...where A is the segment area, x is the number of degrees of arc, r is the radius of the circle, and b and h are base and height of the triangle being subtracted

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