The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]
What is a Trapezium
A trapezium is one pair of parallel sides and one pair of non-parallel sides.
from the diagram we can extract the necessary information needed to find the area of the trapezium.
for the first trapezium (lamp shade)
a = 4 in
b = 6 in
h = 6 in
[tex]A_{1}[/tex] = [tex]\frac{a + b}{2}[/tex] * h
[tex]A_{1}[/tex] = [tex]\frac{4 + 6}{2}[/tex] * 6
[tex]A_{1}[/tex] = [tex]\frac{10}{2}[/tex] * 6
[tex]A_{1}[/tex] = 5 * 6 = 30[tex]in^{2}[/tex]
For the area of the second trapezium (lamp base)
a = 4 in
b = 6 in
h = 4 in
[tex]A_{2}[/tex] = [tex]\frac{a + b}{2}[/tex] * h
[tex]A_{2}[/tex] = [tex]\frac{4 + 6}{2}[/tex] * 4
[tex]A_{2}[/tex] = [tex]\frac{10}{2}[/tex] * 4
[tex]A_{2}[/tex] = 5 * 4 = 20[tex]in^{2}[/tex]
For the area of the third trapezium (lamp base)
a = 6 in
b = 4 in
h = 4 in
[tex]A_{3}[/tex] = [tex]\frac{a + b}{2}[/tex] * h
[tex]A_{3}[/tex] = [tex]\frac{6 + 4}{2}[/tex] * 4
[tex]A_{3}[/tex] = [tex]\frac{10}{2}[/tex] * 4
[tex]A_{3}[/tex] = 5 * 4 = 20[tex]in^{2}[/tex]
The total Area of the trapezium (lamp)
A = [tex]A_{1}[/tex] + [tex]A_{2}[/tex] + [tex]A_{3}[/tex]
A = 30 + 20 + 20
A = 70 [tex]in^{2}[/tex]
Inconclusion The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]
Learn more about Trapezoid : https://brainly.com/question/1463152
