Excerpt from Beast Academy Guide 3D. (C) 2013 www.BeastAcademy.com
To find the area of any right triangle, we
think of the triangle as half of a rectangle.
EXAMPLE
Find the area of the right triangle below.
4 cm
AREA
R igh t Tria ngle s
Any
rectangle
can be split
into two right
triangles.
Two
congruent
right triangles
can always
be arranged
to make a
rectangle.
8 cm
4 cm
We can arrange two copies of the triangle
above to make a rectangle as shown.
8 cm
The rectangle has an area of 4×8=32 sq cm. The
triangle is half the area of the rectangle. So, the
area of the triangle is 32÷2=16 sq cm.
PRACTICE
43.
Find the area of each right triangle below.
44.
mi
43. ___________
29
in
20 in
5 mi
13
12 mi
44. ___________
21 in
45.
15 yd
45. ___________
8m
6m
yd
8 yd
17
46.
10 m
46. ___________
88
Guide Pages: 88-92
Beast Academy Practice 3D
Excerpt from Beast Academy Guide 3D. (C) 2013 www.BeastAcademy.com
AREA
Rig ht Tri a n g les
Right angles are
sometimes marked
with little squares
like these to let you
know they are right
angles.
PRACTICE
Find the area of each shape below.
5 cm
48.
6m
47. ___________
8m
15 m
6m
6 cm
47.
15 m
8m
48. ___________
5 cm
9 ft
9 ft
50.
49. ___________
n
6i
7
5 ft
49.
5 ft
2 in
in
9 in
Two right triangles overlap to make the shape below. The area
where the triangles overlap is a 4 inch by 4 inch square. What is
the area of the whole shape?
8 in
51. ___________
4 in
51.
50. ___________
16 in
6 in
Beast Academy Practice 3D
Guide Pages: 88-92
89
Excerpt from Beast Academy Guide 3D. (C) 2013 www.BeastAcademy.com
AREA
D ot Grid Sha p e s
In each dot grid below, each dot is 1 unit from its
nearest horizontal and vertical neighbor.
We can use
right triangles
to find the area
of a shape
drawn on a
dot grid.
Find the area of the quadrilateral
traced on the dot grid below.
EXAMPLE
We can split the shape into three parts: two triangles and one square.
Each dot is one unit from its nearest horizontal and vertical neighbor.
The square has an area of 3×3=9 square units.
Each triangle is half of a 2 by 3 rectangle. So, the
combined area of the triangles is 2×3=6 square units.
All together, the shape has an area of
9+6=15 square units.
PRACTICE
Find the area of the shaded region on each dot grid below.
53.
52.
52. ___________
53. ___________
54.
55.
54. ___________
55. ___________
90
Guide Pages: 93-98
Beast Academy Practice 3D
Excerpt from Beast Academy Guide 3D. (C) 2013 www.BeastAcademy.com
AREA
Dot Grid Sh a pes
PRACTICE
Find the area of the shaded region on each dot grid below.
56.
57.
56. ___________
57. ___________
58.
59.
58. ___________
59. ___________
60.
61.
60. ___________
61. ___________
Beast Academy Practice 3D
Guide Pages: 93-98
91