Texas Essential Knowledge and Skills (TEKS):
7.8.A*
model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas;
Texas Essential Knowledge and Skills (TEKS):
7.8.B*
explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas; and
Texas Essential Knowledge and Skills (TEKS):
7.9.A
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids;
Texas Essential Knowledge and Skills (TEKS):
7.9.C
determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles; and
Texas Essential Knowledge and Skills (TEKS):
7.9.D
solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net.
7th Grade Math - Area, Surface Area, & Volume Lesson
Area Rectangle = length × width
Area Triangle = (base)(height)
Area Parallelogram = base × height
Area Trapezoid = (base1 + base2)(height)
Area Circle = r2
Example:
First, find the area of each figure. Then, find the sum of those areas.
AreaTRI
=
(base)(height)
=
(16 cm)(13.9 cm)
=
111.2 sq cm
AreaTRAP
=
(base1 + base2)(height)
=
(33 cm + 42 cm)(16 cm)
=
600 sq cm
AreaPARA
=
base × height
=
(42 cm)(10 cm)
=
420 sq cm
Now, add the areas.
111.2 sq cm + 600 sq cm + 420 sq cm = 1,131.2 sq cm
A prism is a three-dimensional figure with parallel, congruent polygonal bases. The volume of a prism is the area of the base, B, times the height, h.
Volume Rectangular Prism = Bh
Volume Rectangular Pyramid = Bh
Volume Triangular Prism = Bh
Volume Triangular Pyramid = Bh
Example:
First, find the area of the base of the prism.
Area
=
bh
=
(3 cm)(4 cm)
=
6 sq cm
Now, find the volume of the prism by multiplying the area of the base times the height.
Volume
=
Bh
=
(6 sq cm)(1.6 cm)
=
9.6 cubic cm
Surface area is the total area of the surface of a three-dimensional figure. The surface area of a prism can be found by adding the areas of its faces.
Example:
First, find the area of each different-sized face.
There are two 4.5-foot by 2-foot faces, two 1-foot by 2-foot faces, and two 4.5-foot by 1-foot faces.
4.5 ft × 2 ft = 9 sq ft
1 ft × 2 ft = 2 sq ft
4.5 ft × 1 ft = 4.5 sq ft
Now, add the areas of the faces. Remember there are two of each size.
7th Grade Math - Area, Surface Area, & Volume Lesson