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Surface area and Volume

Learn how to calculate areas of parallelograms, triangles, trapezoids, rhombuses, and regular polygons with step-by-step examples and formulas. Practice IXL assignments for mastery.

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Surface area and Volume

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  1. Surface area and Volume Ch 11-13 Sol: G.10,12,13,14

  2. Polygon Area Formulas • Parallelogram: • Triangle: • Trapezoid: • Rhombus: • Regular Polygons

  3. Area of a Parallelogram: If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.Example: Find the area of parallelogram STAR. Parallelogram: In this case, we need to find h. Since we know that we have a right angle, and that angle T is 450, we can use trigonometry to find h. Side h is opposite the given angle, and the hypotenuse is given as 9. Now that we have h, the formula is easy.

  4. Area of a Triangle: If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then A = ½bh.Example: Find the area of THE. Triangle:

  5. Area of a Trapezoid: If a trapezoid has an area of A square units, bases of b1 units and b2 units, and height of h units, then A = ½h(b1 + b2).Example: Find the area of trapezoid TRAP. Trapezoid:

  6. Area of a Rhombus: If a rhombus has an area of A square units and diagonals of d1 and d2 units, then A = ½d1d2.Example: Find the area of rhombus SANE, if AE = 12 and SN = 8. Rhombus:

  7. Areas of Regular Polygons If a regular polygon has an area of A square units, a perimeter of P units, and an apothem of a units, then A = ½ (a)(p). The apothem isthe distance from the center of a regular polygon to the midpoint of a side. (For a circle it is the distance from the center to the midpoint of a chord.) Perimeter = apothem = Area = 8 Lesson 9-1: Area of 2-D Shapes

  8. IXL Assignments • S2, S3, and S4 • Must achieve a Smart Score of at least 80. • Begin work on these in class TODAY (now!!) • These are due by the end of the day Friday.

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