# 1 1 2 where d 2 is the longer diagonal and θ is the

• 76
• 100% (1) 1 out of 1 people found this document helpful

This preview shows page 56 - 62 out of 76 pages.

##### We have textbook solutions for you!
The document you are viewing contains questions related to this textbook. The document you are viewing contains questions related to this textbook.
Chapter 8 / Exercise 1
Elementary Geometry for College Students
Alexander/Koeberlein Expert Verified
;1?1?2. where d2is the longer diagonal and θis the angle opposite the shorter diagonal. The Perimeter of a Rhombus If b is the measure of one side of a rhombus, then the perimeter is given by 𝑃 = 4?. Richard T. Eanhart Solid Mensuration: Understanding the 3D Space
##### We have textbook solutions for you!
The document you are viewing contains questions related to this textbook. The document you are viewing contains questions related to this textbook.
Chapter 8 / Exercise 1
Elementary Geometry for College Students
Alexander/Koeberlein Expert Verified
Area of a Rhombus The area of a rhombus may be determined by any of the following ways: The area is one-half the product of its two diagonals.? =12?1?2Note that this expression follows from Formula 1 for the area of quadrilateral, where θ=90Since a rhombus is a parallelogram, the area is also the product of the base times the height. ? = ??The area is twice the area of one of the two congruent triangles formed by one of its diagonals. This is the same method used in finding the area of a parallelogram. ? = ?2???𝜃Richard T. Eanhart Solid Mensuration: Understanding the 3D Space
TRAPEZOID A trapezoid is a quadrilateral with one pair of parallel sides. a b 𝜃𝜃h ? − ?𝟐In the trapezoid shown above, the parallel sides a and b are called bases and h is the height or the perpendicular distance between the two bases. If the non-parallel sides are congruent, the trapezoid is called an isosceles trapezoid.The base angles of an isosceles trapezoid are also congruent. One can observe that the relationship among the sides, height, and base angles of an isosceles trapezoid may be obtained from the right triangle formed by constructing a line from one vertex perpendicular to the opposite side (lower base). Richard T. Eanhart Solid Mensuration: Understanding the 3D Space
A trapezoid which contains two right angles is called a right trapezoid. The trapezoid on the right is an example of a right trapezoid. a b-a h b Area of a Trapezoid The area of a trapezoid is equal to the product of the mean of the bases and the height. In symbols, the area is given by the formula ? =12? + ? h. The median of a trapezoid is the line segment parallel to and midway between the bases of the trapezoid. Thus, ? =?:?2and A=mh. Richard T. Eanhart Solid Mensuration: Understanding the 3D Space
TRAPEZIUM A trapezium is a quadrilateral with no parallel sides. In finding the area of a trapezium, you may use any of the three formulas for the area of a quadrilateral. Example 8 Find the area and perimeter of a square whose diagonal is 15 units long. a a 15 First find the length of a side of the square using the formula ? = ?2. Thus, the measure of the side of the square is ? =1522units. Therefore, the area is A=112.5square units and the perimeter is 𝑃 = 302, or 42.43 units. Richard T. Eanhart Solid Mensuration: Understanding the 3D Space
Example 9 The side of a square is x meters. The midpoints of its sides are joined to form another square whose area is 16 m2. Find the value of x and the area of the portion of the bigger square that is outside the smaller square.
• • • 