MAP4C - Lesson 5 Assignment: Area, Volume, and Surface Area

This document provides complete solutions to the MAP4C Lesson 5 assignment, focusing on geometric shape calculations. The assignment covers finding the surface area of an isosceles triangular prism, calculating the cross-sectional area of a staircase, and determining the area and volume of various shapes. Step-by-step solutions are provided for each problem, including diagrams, formula identification, and detailed calculations. The assignment includes questions related to area, volume, and surface area, offering comprehensive support for students studying geometry and related mathematical concepts. The solutions are presented in a clear and organized manner, making it easy for students to understand the concepts and master the material. The assignment covers a range of problems, from basic area calculations to more complex volume and surface area determinations. The document serves as a valuable resource for students seeking to improve their understanding of geometric concepts and excel in their mathematics coursework.

MAP4C Lesson 5 Assignment Answers
Surface area of isosceles triangular prism to two decimal places.
17.5in
21.2inn
16.4in
21.2in
16.4in
c
Diagram 1
Diagram 2
To find the value “c” in diagram 1;
a2+ b2=c2
21.22 +( 16.4
2 )
2
=c2=516.68∈¿
c= √516.68∈¿=22.73∈¿ ¿
To find total area of A, B, C we combine the
lengths of the rectangles.
Total length= (22.7+22.7+16.4) =61.8in
Total Width= (17.5in)
Total area of A, B, C= (61.8×17.5) =1081.5in2
Area of triangle (diagram 2)
A=1
2 × b × h
A=1
2 × 16.4 ×21.7=173.84in2
(Two triangles)= (186.14 × 2) =347.68in2
Total surface area of diagram 1 is
A
B
C
c
Choice “b”
Question 2
Cross sectional
area of staircase
12cm
12cm
Area of the cross section of staircase; the cross
section has six cubes of 12 cm and the front has
6 rectangle.
Area of each cube is;
A1=12 ×12=144 cm2
Total area= (144 ×6) =864cm2
For the two sides= (864 × 2) = 1728cm2
Area of each rectangle
A2= (120 × 12) = 1440cm2
Total area=1440 × 6 = 8640 cm2
Total area of the staircase
= (8640 +1728) = 10368 cm2
1.2m=120cm
12cm
Choice “b”
Question 1

Question 3
(23-15)=8 m
8 m
15 m
We first find the area of the cross section
We find the area of the rectangle
A=length ×width
8×15=120m2
Finding area of triangle
A= 1
2 ×b × h= 1
2 × 8 ×8=32m2
Total area of the cross section
= (32 + 120)m2 =152m2
Volume of concrete riser
152×20=3040m3
$10.99 = 13m3
Cost of building 3040× 10.99
13 =$ 2569.9692
≈ $ 2570.97
Choice “c”
Question 4
CA
15m 11.31m
20m
8m
36m
20m
11.31m
Area of A= (L ×W )
A= (20×8) m2=160m2
Area of B (trapezium) = 1
2 ×(b¿¿ 1+b2)×h ¿
1
2 ×(15+23)× 8=152 m2
They are two=152×2=304m2
Area of C (rectangle)
=Area= L ×W
11.31× 20=226.2m2
Area of rectangle D
Area= L ×W
15 ×20=300 m2
Total area=
¿2
Cost= 1980.4 ×24.97
80 =$ 618.18 m2
8m
B
20mD
Choice “a”

Question 5
0.7m
1.2m
0.9m
Volume of the Sirius’ doghouse is
=Cross sectional area ×length
Cross section area of the triangle=
1
2 ×b × h= 1
2 × 0.9× 0.5=0.225 m2
Cross section area of the rectangle=
length ×width=0.7× 0.9=0.63 m2
Total cross section= (0.63+0.225) =0.855m2
Volume= 0.855 ×1.5=1.28 m3
Volume of the Sirius’ doghouse is 1.28 m3
Question 6
1.5m
1.5m
0.9m
0.67
0.5m 0.67m
0.7m
0.67m
m
0.7m
0.5m
0.45m
Hypo
Step1
From the triangle we find the hypotenuse = (a2+b2=c2)
=0.52 +0.452 =hyp2=0.4525m2
Hyp=√0.4525=0.6727 m
Step2
The figure has A1, A2, A3, A4, A5 making a large rectangle
hence
Length= (0.7+0.9+0.7+0.67+0.67) =3.64m, Width=1.5m
Area= l ×w= ( 3.64 ×1.5 ) =5.46 m2
Area of B
Cross section area of the triangle=
1
2 ×b × h= 1
2 × 0.9× 0.5=0.225 m2
Cross section area of the rectangle=
length ×width=0.7× 0.9=0.63 m2
Total cross section= (0.63+0.225) =0.855m2
For both sides=(0.855 ×2)=1.71 m2
Total surface area is
5.46+1.71=7.17 m2
A1
A5
A4
A3
A2 B