Questions and Answers
What is the area of parallelogram RSTU?
32
How does the area of triangle ABC compare to the area of parallelogram GHJK?
The area of △ABC is 2 square units greater than the area of parallelogram GHJK.
What is the measure of the radius, c, rounded to the nearest hundredth?
12.36 cm
What is the area of trapezoid ABCD?
Signup and view all the answers
What is the measure of angle BCD?
Signup and view all the answers
What is the value of x if the area of a shaded rectangle section is 63 square units?
Signup and view all the answers
Which polygon is a concave octagon?
Signup and view all the answers
What is the approximate area of the regular hexagon with a radius of 4 in?
Signup and view all the answers
What is the measure of ∠B?
Signup and view all the answers
What is the value of x in the shaded rhombus with area 60 square units?
Signup and view all the answers
What is the area of triangle LMN?
Signup and view all the answers
What is the area of parallelogram RSTU?
Signup and view all the answers
What is true about the areas of the trapezoids created from parallelogram ABCD?
Signup and view all the answers
What is the measure of angle x in the regular nonagon?
Signup and view all the answers
What is the area of the equilateral triangle with apothem 2.16 cm and perimeter 22.45 cm?
Signup and view all the answers
What is the perimeter of the regular pentagon with an area of 6.9 cm2?
Signup and view all the answers
What is the area of parallelogram ABCD?
Signup and view all the answers
What type of polygon is shown?
Signup and view all the answers
What is the area of kite ABCD if AC = 10 and BD = 6?
Signup and view all the answers
What are the dimensions of the rectangle Michael should draw to find the area of parallelogram ABCD?
Signup and view all the answers
The final angle of a heptagon with the sum of all but one interior angle being 776° must measure ___ degrees.
Signup and view all the answers
What is the value of x?
Signup and view all the answers
What is the approximate area of a regular decagon with a radius of 8 cm?
Signup and view all the answers
What is the value of x in rhombus ABCD if the area is 72 square units, EC = 8 units and DB = x - 1?
Signup and view all the answers
Which polygon has an interior angle sum of 1080°?
Signup and view all the answers
Study Notes
Area Calculations
- Area of parallelogram RSTU is 32 square units.
- Triangle ABC's area is 2 square units greater than that of parallelogram GHJK.
- Area of trapezoid ABCD is 12 square units.
- Area of triangle LMN is 12 square units.
- Area of parallelogram ABCD is 20 square units.
- Area of rhombus ABCD is 72 square units; requires diagonal measures for calculations.
Polygon Properties
- The radius of a regular pentagon is approximately 12.36 cm.
- Hexagon with a radius of 4 in. has an approximate area of 42 in².
- The regular pentagon has an area of 6.9 cm², which corresponds to a perimeter of 10 cm.
- Area of a regular decagon with a radius of 8 cm is approximately 188 cm².
Angle Measures
- Measure of angle BCD is 140°.
- Measure of angle x in a regular nonagon is 40°.
- Measure of angle B in a regular polygon is 108°.
- The sum of all but one interior angle in a heptagon is 776°; the missing angle is 124°.
Shape Characteristics
- A section of a rectangle has a shaded area of 63 square units, and the corresponding value of x is 11.
- A kite with diagonals AC = 10 and BD = 6 has an area of 30 square units.
- A concave heptagon is identified among various polygon types.
Problem Solving Techniques
- To find area using containers, Michael draws a rectangle around parallelogram ABCD, measuring 4 units by 4 units.
- Two trapezoids formed in parallelogram ABCD have equal areas, each being half of the parallelogram's total area.
- Application of trigonometric ratios may be required in some scenarios for figuring out polygon measurements.
Additional Measurements
- The shaded area of a rhombus model is 60 square units, with x equating to 8 units.
- In context of area relationships, the area of a parallelogram was mentioned multiple times with differing values (21 and 32 square units).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This set of flashcards is designed to help learners master the concepts of area calculations including areas of parallelograms, triangles, and regular pentagons. Each card presents a question that challenges the understanding of geometric principles and trigonometric ratios. Perfect for review and self-assessment on area concepts.
