Practice - Beast Academy
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
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
