Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
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1 Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane figures have equal areas, then they are congruent. (3.) TRUE or FALSE: If two plane figures are congruent, then they have equal areas. (4.) Find the area of a rectangle that is 1 foot long and 5 inches wide. (5.) Use the Area-Addition Postulate to draw a conclusion. Find if A RUS = 45 in A S and A = 3 in. R (6.) With sides and corresponding altitudes having the indicated lengths, find the area of parallelogram WXYZ. (.) Find the area of the right triangle whose sides measure 6 cm, 8 cm, and 10 cm. (8.) The area of a triangle whose sides measure 5 inches, 1 inches, and 13 inches is 30 square inches. Find the length of the altitude to the 13 inch side. (9.) In the figure, a square with sides of length 3 inches lies inside a second square with sides of length 6 inches. Find the area of the shaded region. (10.) Given that there are 1 inches in one foot, how many square inches are in one square foot?
2 Section. Perimeter and Area of Polygons (1.) State the formula for perimeter P of an equilateral triangle whose sides have length s. (.) Find the perimeter of the rectangle shown. One side has length 3" while the diagonal has length 5". (3.) The perimeter of an isosceles triangle is 3 cm. If the length of the base is 8 cm, find the length of each leg. (4.) The area of a quadrilateral whose diagonals are perpendicular is given by A= 1 d1 d. For which type(s) of quadrilateral can this formula be used rectangle, rhombus, kite, trapezoid? (5.) Find the area of a rhombus whose diagonals measure 8 feet and 1 feet. (6.) The 16 inch diagonal of a kite separates the 1 inch diagonal into parts measuring 6 inches and 15 inches. Find the perimeter of the kite. (.) Use Heron s Formula A= s( s a)( s b)( s c) to find the area of the triangle whose sides measure 9 cm, 10 cm, and 1 cm. (8.) Find the area of a trapezoid with bases of lengths 1 inches and 8 inches and an altitude of length 6 inches. (9.) The trapezoid whose bases have lengths 10 inches and 14 inches has the area 10 in. Find the length of its altitude. (10.) Find the perimeter of a regular pentagon if a side measures 8 inches.
3 Section.3 Regular Polygons and Area (1.) In which type(s) of quadrilateral can a circle be inscribed rectangle, square, trapezoid, rhombus? (.) About which type(s) of quadrilateral can a circle be circumscribed rectangle, square, trapezoid, rhombus? (3.) A regular dodecagon has 1 sides. Find the measure of each central angle of the polygon. (4.) Each central angle of a regular polygon measures 40. How many sides does the polygon have? (a) (5.) For regular ABCDEF, name: (b) (a) an apothem (b) a radius (6.) Each side of a square has length 8 centimeters. Find the length of the apothem of the square. (.) Each side of a square has length 8 centimeters. Find the length of the radius of the square. Exercises 6 & (8.) Quadrilateral RSTV is inscribed in a O. How are the opposite angles ( like R and T ) related to each other. (9.) A regular hexagon has sides of length 4 inches. If the length of the apothem is 3 inches, what is the area of the polygons? (10.) A regular polygon has perimeter 3 cm and an area of 100 cm. Using the formula A= 1 ap, find the length of the apothem.
4 Section.4 Circumference and Area of a Circle (1.) What symbol is used to represent the numerical ratio between the circumference and the length of the diameter of a circle? (.) In a circle of radius 5 meters, find an expression for the exact circumference of the circle. (3.) In a circle with diameter 1.8 inches, find the approximate circumference of the circle correct to two decimal places. Let π (4.) Using π, find the length of a 90 arc in a circle whose radius measures 16 cm. (5.) For a circle of radius 6 meters, find the exact area of the circle. (6.) For a circle of radius cm, use π to approximate the area of the circle. (.) The exact area of a circle is 36 π cm. Find the length of the radius of the circle. (8.) For the annulus shown, the inside radius is 3 inches while the outside radius is 4 inches. Find the exact area of the annulus. (9.) A convicted criminal has traveled 50 miles from the jail from which he escaped. To the nearest square mile, how large is the area that should be searched? Use the calculator value of π. (10.) A square is inscribed in a circle. If the diagonal of the square measures 6 inches, what is the exact area of the circle?
5 Section.5 More Area Relationships in the Circle (1.) For a sector, what is the measure of the central angle used to represent the common fraction 1 4? (.) In a circle of radius 6 cm, find the exact area of the sector whose central angle measures 10. (3.) In a circle of radius 6 cm, find the exact perimeter of the sector whose central angle measures 10. Exercises & 3 (4.) Using π, find the approximate area of the semicircular region with a diameter of length 14 cm. (5.) Using π, find the approximate perimeter of the semicircular region with a diameter of length 14 cm. (6.) In a circle whose radius is 6 cm, the exact area of a sector is 9 π cm. Find the measure of the central angle of the sector. (.) In A = 8.1 ft and the area of the sector XOY bounded by radii OX and OY and XY is 1.64 ft, find the area of the shaded segment. (8.) Use A= 1 rp to find the area of a triangle whose sides measure 6 inches, 8 inches, and 10 inches. The radius of the inscribed circle is inches. (9.) The area of a triangle with sides of 4 cm, 13 cm, and 15 cm is 4 cm. Find the length of the radius of the inscribed circle. (10.) A drop-leaf table has a square top with two semicircular leaves at the ends. To two decimal places, find the area of the table s surface when the leaves are extended as shown. Use π 3.14.
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Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
IMO Geomety Problems. (IMO 1999/1) Determine all finite sets S of at least three points in the plane which satisfy the following condition:
IMO Geomety Problems (IMO 1999/1) Determine all finite sets S of at least three points in the plane which satisfy the following condition: for any two distinct points A and B in S, the perpendicular bisector
Lesson 1.1 Building Blocks of Geometry
Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.