7.8.A* 7.8.B* 7.9.a 7.9.c 7.9.d

Area, Surface Area, & Volume 7th Grade

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.

Area Rectangle = length × width

Area Triangle =

\frac{1}{2}

(base)(height)

Area Parallelogram = base × height

Area Trapezoid =

\frac{1}{2}

(base_₁ + base_₂)(height)

Area Circle =

π

r^²

Area_{_TRI}	=	$\frac{1}{2}$ (base)(height)
	=	$\frac{1}{2}$ (16 cm)(13.9 cm)
	=	111.2 sq cm

Area_{_TRAP}	=	$\frac{1}{2}$ (base_₁ + base_₂)(height)
	=	$\frac{1}{2}$ (33 cm + 42 cm)(16 cm)
	=	600 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 =

\frac{1}{3}

Volume Triangular Prism = Bh

Volume Triangular Pyramid =

\frac{1}{3}

First, find the area of the base of the prism.

Area	=	$\frac{1}{2}$ bh
	=	$\frac{1}{2}$ (3 cm)(4 cm)
	=	6 sq cm

Area, Surface Area, & Volume

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.

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