Covering and Surrounding Review Answer Key
1. Choice a. (6x10) + (2x3) because you break the shape into 2 rectangles, find the area of each, and add up the two areas.
2. Choice b. The perimeter of the triangle is less than the perimeter of the rectangle. Explanation- The perimeter of the rectangle is 18 units, and 2 sides of the triangle are 4 and 5 units (total of 9 units), so it is unlikely that the last side will be more than 9 units.
3. c. 102 square ft. Remember that the area of a triangle is base x height divided by 2!
4. The PERIMETER needs to equal 20. That’s the distance around the rectangular shelter.
a.)
length / width9 / 1
8 / 2
3 / 7
4 / 6
5 / 5
b.) She should choose the 5 x5 shelter because 5x5 = 25 square ft.
c.) She should choose the 1x9 shelter because 1x9 = 9 square ft.
5. a.) Area= b times h b.) Area= 33 square units
A= 7 x 4= 28 square units P= 28 units
P= 7 x2 + 4x2= 22 units
c.) Area =length x width = 9x9= 81 sq. ft. d.) A= l times w = 20x15= 300 sq. in.
Perimeter= 9 x 4= 36 ft Perimeter= 20x2 +15x2= 70 in.
6. Yes, she could be correct. If she had a 4x3 rectangle, then the area would be 4x3, which is 12 square units and the perimeter would be 4 + 4 + 3 + 3, which equals 14 units.
7. a.) The missing sides are 3 cm (the horizontal one) and 5 cm (vertical one). The perimeter= 1 + 5 + 1 + 3 + 2 + 1 + 3 + 4 + 5 + 3= 28 cm.
b.) I broke it up into 3 rectangles and added the areas together to get an area of 27 cm2. 12 + 10 + 5 = 27 square cm.
8. Area of 100 1x100, 2x50, 4x25, 5x20, 10x10
a.) The largest perimeter would be the 1x100 rectangle. (P= 202 units)
b. ) The smallest perimeter would be the 10x10 rectangle (P=40 units)
9. a.) A= 10x8=80 square units P= 10x2 + 9x2= 38 units
c.) A= 8 x 1= 8 square units P= 8x2 + 5x2= 26 units
10. For the perimeters, you would need to measure the lengths of the sides and add them together. It is a bit confusing because the original problem was on centimeter grid paper, but I shrunk it to take up less space. As long as you know how to find perimeter, you should be okay.
and now for the areas…
a.) A= 4x5÷2- 10 square units
b.) A=5x3÷2= 7.5 square units
c.) A= 5x7÷2= 17.5 square units
d.) A= 5x4÷2= 10 square units
11. a. If one side = 2.2 cm, then the opposite side = 2.2cm. If you add those together, it equals 4.4cm. The total perimeter is 14.4 cm, so if you subtract 14.4-4.4, that will equal what the other two sides add up to . 14.4-4.4=10cm, so the other two sides must be equal and add up to 10cm, so each one is 5cm long.
b.) The area would be the base times the height.
The base is 5cm and the height is 2 cm, so 5x2=10 centimeters squared.
12. Perimeter is measured in regular units because perimeter is a measurement of length. It’s the length or distance around a shape or figure. Since length is measured in regular units (miles, meters, centimeters, feet, etc.), perimeter is measured in them too. Perimeter has just one dimension- length.
Area is different. Area measures the space inside a 2 dimensional space or figure. For example, you could find the area of a carpet needed to cover a floor. Because area takes into consideration 2 dimensions, length and width (and is not one dimensional like perimeter), the units are 2 dimensional units (Units Squared).
Perimeter is surrounding, while area is covering.
13. Just make sure you drew 3 triangles that each had a base of 5 box lengths and were 4 units box lengths high. I can check them for you tomorrow if you’re not sure if you did it correctly.