A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.

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1 Geometry - Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle ABGF is the same area as Y ABCD. h D F C G Ex : Find the area and perimeter of Y RSTU. R 30 o S 4 in. U 3 in. T Ex : The devanderdutchma s are planning to sod some parts of their yard. Find the number of square 00 ft. yards of grass needed. 50 ft. vegetable garden 50 ft. 40 ft. 60 ft. grass 50 ft. 00 ft. garage house and walkways B. Parallelograms on the Coordinate Plane. Using properties you know about and slopes and distance formulas, you can find areas of quadrilaterals on the coordinate plane.

2 Ex 3: The vertices of a quadrilateral are located at A( -,3), B(4,), C(3,-), D(-3,0). a.) Determine whether the quadrilateral is a square, a rectangle or a parallelogram. b.) Find the area of quadrilateral ABCD. HW: Geometry - p odd, 6-8, 3-3, 37-45, Hon: 33-35

3 Geometry - Areas of Triangles, Trapezoids, and Rhombi A. Areas of Triangles. The area of the rectangle is A = bh, so the area of the triangle is one-half the area of the rectangle.. The area of the triangle is A = bh. Ex : Find the area of quadrilateral ABCD if AC = 35, BF = 8, and DE = 0. A E F B C D B. Areas of Trapezoids and Rhombi. The area of a trapezoid is given by the formula A = ( b + b ) h A D C B Ex : Find the area of trapezoid RSTU with vertices R(4, ), S(6, -), T(-, -) and U (-, ).. If a rhombus has an area of A square units, and diagonals of d and d, then A = dd.

4 Ex 3: Find the area of rhombus MNPR with vertices at M(0, ) N(4, ), P(3, -) and R(-, -3). Ex 4: Rhombus RSTU has an area of 64 square inches. Find US if RT = 8 inches. R S U T Ex 5: Trapezoid DEFG has an area of 0 square feet. Find the height of DEFG. D 0 feet E G 0 feet F HW: Geometry - p odd, 38-4, 5-56, 6-64, 65-7 odd, Hon: 44, 45, 6

5 Geometry -3 Areas of Regular Polygons and Circles A. Areas of Regular Polygons. The segment drawn from the center of a regular perpendicular to the side of the polygon is called an apothem. a. The area of the little triangle would be A = bh. a. How many times would you need to multiply the area of the little triangle by to get the area of the entire polygon? b. How many sides are in the polygon? b a c. What would the number of sides multiplied by b be equal to? 3. If a regular polygon has an Area of A square units, a perimeter of P units, and an apothem of a units, then A = Pa. Ex : Find the area of a regular pentagon with a perimeter of 0 cm. B. Areas of Circles. If a circle has an area of A square units, and a radius of r units, then A = π r. Ex : An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the side of an umbrella on each side, then find the area of the cover in square inches and then square yards. 8 in 7 in

6 Ex 3: Find the area of the shaded region. Assume the triangle is equilateral. Round to the nearest tenth. 7cm HW: Geometry -3 p odd, 3-7, 30-3, 34-35, 39, 57-6, odd, 66-7 Hon:, 40-4, 44, 49-54

7 Geometry -4 Areas of Irregular Figures A. Irregular Figures. Postulate - The area of a region is the sum of all its non-overlapping pars. Ex : Find the area of the figure in square feet, round to the nearest tenth. 3 ft. 6 ft. 5 ft. Ex : A rectangular rose garden is centered in a border of a lawn. Find the area around the garden in square feet. 5 ft. 00 ft. Rose Garden 0 ft. 5 ft. B. Irregular Figures on the Coordinate Plane. The formulas for regular figures do not apply to irregular figures, so break down the irregular figures to ones that you know.

8 Ex 3: Find the area of the quadrilateral given A (-3, 0), B(0, 5), C(3, 0), and D(0, -4). HW: Geometry -4, p , 30-3, 34-37, 39-4 Hon: 5-8

9 Geometry -5 Geometric Probability A. Geometric Probability. Probability that involves a geometric measure such as length or area is called geometric probability.. The probability that a point is in region B, which is in the interior of region A is area of region B P( B ) = area of region A A B Ex : A game board has consists of a circle inscribed in a square. What is the chance that a dart thrown at the board will land in the shaded area? in B. Sectors and Segments of Circles. A sector of a circle is a region of a circle bounded by a central angle and its intercepted arc. Ex : a.) Find the area of the 35 and 45 degree sectors. 80 o b.) Find the probability that a point chosen at random lies in those two areas. 45 o 90 o 50 o 60 o 35 o 8 in

10 Ex 3: A regular hexagon is inscribed in a circle with a diameter of. a.) Find the area of the shaded region. b.) Find the probability that a point chosen at random lies in the shaded region. HW: Geometry -5 p odd, 6, 7-3 odd, 4-5, Hon: 6-9