Aim #1: What are the properties of area?
CC Geometry H
Do Now: Two congruent triangles are shown:
a. Calculate the area of each triangle.
b. Circle the transformations that, if applied
to the first triangle, would always result in a
new triangle with the same area.
Translation
Rotation
Dilation
Reflection
c. Explain your answer to (b).
1. Calculate the area of the figure below. Show all work. Explain how you
determined the area.
2. a) ΔABC and ΔDEF overlap and form ΔDGC. Calculate the area of figure ABGEF.
AD = 4, DC = 3, and CF = 2. Show all work and explain how you determined the area
of the figure.
b) What region is the union (∪) of ΔABC and ΔDEF? ________________
c) What region is the intersection (∩) of ΔABC and ΔDEF? _______________
3. A rectangle with dimensions 21.6 x 12 has a right triangle with a base 9.6 and a
height of 7.2 cut out of the rectangle.
a) Find the area of the shaded region.
b) Explain how you determined the area of the shaded region.
A polygonal region is the union of finitely many non-overlapping triangular regions.
The area of a polygonal region is the sum of the areas of the triangles.
4. Some polygons have been drawn below. Show that each is the union of
triangles.
5. Compute the area of the figure from (1) with the rectangle divided into two
congruent triangles. Is the area changed from the result you found in (1)?
6. Wood pieces in the followings shapes and sizes are nailed together in order to
create a sign in the shape of an arrow. The pieces are nailed together so that the
rectangular piece overlaps with the triangular piece by 4 in. What is the area of
the region in the shape of the arrow?
arrow-shaped sign
7. If two 2 x 2 square regions S1 and S2 meet at midpoints of sides as shown, find
the area of the region, S1 ∪ S2.
"UNION"
8. The figure shown is composed of a semicircle and a non-overlapping equilateral
triangle, and contains a hole that is also composed of a semicircle and a nonoverlapping equilateral triangle. If the radius of the larger semicircle is 8, and
the radius of the smaller semicircle is
that of the larger semicircle, find the
exact area of the figure and the area rounded to the nearest whole number.
Let's Sum it Up!
The Properties of Area
-The area of a set in the plane is a number, greater than or equal to zero, that
measures the size of the set and not the shape.
-A polygonal region is the union of finitely many non-overlapping triangular regions.
The area of a polygonal region is the sum of the areas of the triangles.
-Congruent triangles have the same area.
-The area of the union of two regions is the sum of the areas minus the area of
the intersection.
-The area of the difference of two regions where one is contained in the
other is the difference of the areas.
Name ______________________
CC Geometry H
Date __________________
HW #1
1. Two squares with side length 5 meet at a vertex and together with segment AB
form a triangle with base 6 as shown. Find the area of the shaded region.
5
5
6
2. If two 6 x 6 square regions S1 and S2 meet at midpoints of sides as shown, find
the area of the square region, S1 ∪ S2.
3. Find the area of the shaded region:
4. Find the area of the shaded polygonal regions:
a)
b)
Mixed Review:
1. A blimp is 4 minutes away from flying over a 50 foot tall football stadium. The
blimp is flying at an altitude of 160 feet. The 50 foot tall stadium can be viewed
o
from the blimp at a 35 angle of depression. Determine the horizontal distance
the blimp will travel to the nearest foot in the next 4 minutes.
2. In ΔSCU shown, points T and O are on SU and CU, respectively. Segment OT is
drawn so that ≮C ≅ ≮OTU. a) Write a similarity statement describing which two
triangles are similar. b) If TU = 4, OU = 5, and OC = 7, what is the length of ST?
S
T
C
O
U
3. a) Show that ΔABC is congruent to ΔPQR with a reflection followed by a
translation. (No construction tools needed).
b) Explain why the triangles
are congruent.