Essential Math 7B Unit 2 Review: Geometric Measurement

Essential Math 7B Unit 2 Review: Geometric Measurement

Go get these things now:

Calculator

Paper

Pencil

Topics we will review:

Choosing and using area formulas (parallelogram, triangle, trapezoid, square, circle, and composite shapes)

Finding cross sections of solids

Finding Surface Area of pyramids, rectangular prisms, triangular prisms, and cylinders.

Finding the volume of cylinders, triangular prisms, and real world cylinders and rectangular prisms.

Do you have these memorized? No?

No worries! WRITE THEM DOWN on a piece of paper. (Yes, now) Then look at that paper during your test!

Multiple Choice

Find the area of this triangle. (click the picture to make it bigger) Use the formula and a calculator.

 $A=bh\div2$  

• 48 square units

• 24 square units

• 30 square units

• 60 square units

Multiple Choice

Find the area of a parallelogram with base 9 cm and height 10 cm. Use the formula and be careful with the units on your final answer!

 $A=bh$  

• 19 cm

• 19 square cm

• 90 cm squared

• 90 cm

Trapezoids!

*have exactly one pair of parallel sides that are called "bases."

*their height is the bases' distance apart

 $A=\left(b_1+b_2\right)h\div2$  


Add the bases, multiply by the height, divide by 2.

Poll

Great! So the bases are 10 and 5, and the height is 11. If we use the formula, that gets us this:

 $A=\left(\left(b+b\right)h\right)\div2$  

 $A=\left(\left(10+5\right)10\right)\div2$     SO what do you think?

Multiple Choice

Great! So the bases are 10 and 5, and the height is 11. If we use the formula, that gets us this:

 $A=\left(\left(b+b\right)h\right)\div2$  

 $A=\left(\left(10+5\right)10\right)\div2$     OK! Let's do this...

•  $\left(15\right)10\div2=25\div2=13.5\ units^2$  

•  $\left(15\right)10\div2=150\div2=75\ units^2$  

Multiple Choice

 $A=\left(b+b\right)h\div2$  

Find the area of the trapezoid. Use the formula and a calculator.

• 65 square cm

• 18 square cm

• 32.5 square cm.

For Area and Circumference of Circles, use these formulas

Don't forget to square the radius first when you find the area (GEMDAS, exponents before multiplication).

Multiple Choice

Find the area of a circle with radius 10 meters. THINK FAST!

•  $A=3.14\times10^2$  

•  $A=2\times3.14\times10$  

Multiple Choice

Find the area of a circle with radius 10 meters.  $A=3.14\times10^2$  

• 31.4 square meters

• 314 square meters

• 157 square meters

Multiple Choice

Find the circumference of a circle with radius 7 ft. THINK FAST!

•  $C=3.14\times7^2$  

•  $C=2\times3.14\times7$  

Multiple Choice

Find the circumference of a circle with radius 7 ft. Use a calculator. $C=2\times3.14\times7$  

• 6.28 square feet

• 17.34 square feet

• 43.96 square feet

Be Careful!!

Both of those formulas use the radius. Sometimes they don't show the radius, just the diameter.

If the diameter is 18, CUT IT IN HALF to get the radius (9 inches).

Multiple Choice

 $A=\pi r^2$  

Find the area of this circle. Use the formula

• 254.34 square inches

• 113.04 square inches

Multiple Choice

Which composite is made of a half-circle (semicircle) and a rectangle?

For this one, add the two triangles to the rectangle.

 $triangle:\ 2\times3\div2=6\div2=3$  

 $rec\tan gle:\ 11\times4=44$  
 $triangle:\ 3\times3\div2=9\div2=4.5$  
Total:  3 + 44 + 4.5 = 51.5 square feet

Now that we can find area, we can find SURFACE area.

The surface area of a solid is the total area of all the faces of the solid.

Multiple Choice

Find the surface area of this triangular prism from the net.

• $6\times6+4\left(6\times12\right)$

  square + 4 triangles,

• $6\times6+4\left(6\times12\div2\right)$ square + 4 triangles

• $6\times6+6\times12$
  square + triangle

Multiple Choice

 $6\times6+4\left(6\times12\div2\right)$  

Ok! But what now?

Multiple Choice

 $6\times6+4\left(36\right)$  

Ok! Go ahead and finish it now:

• 2,880 square cm

• 324 square cm

• 4,320 square cm

This picture explains the Surface Area formula for rectangular prisms.

Remember to work inside the parentheses first and to multiply before adding while you're in there!

Multiple Choice

 $SA=2\left(lw+lh+wh\right)$  

Find the surface area of this rectangular prism using the formula with  $l=4$   $w=3$   $h=5$  

• 12 square units

• 60 square units

• 94 square units

Cylinder Surface Area

2 circles, each   $\pi r^2$  

1 rectangle with  $l=$  the height of the cylinder and  $w=2\pi r$  (the circumference of the circle)

Can with no lid? Frosting cake? Only find ONE circle.

Multiple Choice

Try the Cylinder. Its formula for Surface Area is

 $2\pi r^2+2\pi rh$  

•  $2\left(3.14\right)3^2+2\left(3.14\right)\left(3\right)\left(4\right)$  

•  $2\left(3.14\right)4^2+2\left(3.14\right)\left(4\right)\left(3\right)$  

Multiple Choice

 $2\left(3.14\right)3^2+2\left(3.14\right)\left(3\right)\left(4\right)$  

Ok! Go ahead and do it. Remember GEMDAS.

• 56.52 square feet

• 131.88 square feet

• 150 square feet

Volume of Cylinders, Triangular Prisms, and Rectangular Prisms

Find the area of the base (triangle, circle, or rectangle) then multiply by the height.

We don't have time to do these...

but they are much easier than the surface area formulas!

Let's go back to the live lesson room for some downloads and one video to watch later.