To find: The surface area of the given composite
Answer to Problem 35PPS
The surface area of the given composite solid
Explanation of Solution
Given Information:
Dimensions of the given solid is shown in the given diagram
Formula used:
Area of trapezoid:
A trapezium is a quadrilateral in which one pair of sides are parallel, but the other pair of opposite sides are non-parallel.
Area, A =
Calculation:
The given solid can be identified as trapezoidal prism. That is it has two congruent trapezoids for its top and lower base. It have four rectangles that connect the corresponding sides of the bases.
- Area of trapezium at base:
- Area of rectangle at bottom:
- Area of rectangle at top:
- Area of rectangle at left:
- Area of rectangle at right:
The parallel-sides have length 13 and 20 cm. Also the distance between them is 21 cm.
Length = 20 cm
Breadth = 28 cm
Length = 13 cm
Breadth = 28 cm
Length = 21 cm
Breadth = 28 cm
To find the missing edge along the right side draw a vertical line down from the upper right corner as shown below.
To find the value of x we can use Pythagoras theorem
That is,
∴
Total surface area of the solid is the sum of the areas of the base and area of lateral faces.
Chapter 12 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
Trigonometry (11th Edition)
Elementary Algebra
Introductory Statistics
Mathematics All Around (6th Edition)
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning