6th Grade Math Textbook, Fundamentals

4 mm 4 mm

9 mm

slant height

7 ft

8 ft

8 ft

8 ft

slant height

Lesson 11-4 for exercise sets. &KDSWHU 

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Find the surface of each pyramid. Round to the nearest tenth, if necessary.

1.square pyramid 2.triangular pyramid

3.Discuss and Write Describe the difference between the slant height of a

pyramid and the height of a pyramid.

Some dimensions of a figure may not always be given or the

dimensions need to be expressed as different units of measure.

Find the surface area of this tetrahedron (triangular pyramid)

in square millimeters.

The dimensions of the pyramid are given in centimeters.

The height of the equilateral triangular base is notgiven.

Find the height of the equilateral triangular base. Use the

Pythagorean Theorem. The height of the equilateral base

divides the equilateral triangle into two congruent right

triangles, each with a base of 3 cm and a hypotenuse of 6 cm.

62  32 x^2 Use the Pythagorean Theorem.

62  32  32 x^2  32 Subtract 3^2 from both sides to isolate x^2.

62  32 x^2 Evaluate the exponential expressions.

36  9 x^2 Simplify.

27 x^2 Take the square root of both sides.

x

x 5.2

So the height of the equilateral triangular base is about 5.2 cm.

Convert each dimension from centimeters

to millimeters.

60 mm

50 mm

52 mm

So the surface area of the tetrahedron is about 6060 square millimeters.

27 93 33•

33

52 .•cm^101 cmmm

5 cm•^101 cmmm

6 cm•^101 cmmm

27

Remember:The Pythagorean

Theorem states that in a right

triangle, the square of the

hypotenuse equals the sum of

the squares of the legs.

Think

The lateral faces are congruent isosceles

triangles. The base is an equilateral triangle.

60°

6 cm 6 cm

6 cm

5 cm

5 cm 5 cm

4 cm

30°

3 3√

6 cm

3 cm 3 cm

6 cm 6 cm

Calculate the surface area.

• Find the Lateral Area (LA).

LA (^3) ( (60)(50))
3(1500) 4500 mm^2

• Find the Area of the Base
  A (60)(52) 1560 mm^2

S 1560  4500 6060 mm^2

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2

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