Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now a smaller triangle: base = 10 cm, height = 6 cm. First, what is 10 × 6? Yes, 60. Now take half: what is ½ × 60? Yes, 30. So the area is 30 square centimeters. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is the area of a rectangle 8 cm long and 5 cm wide?

   1. A40 square cm
   2. B26 square cm
   3. C13 square cm
   4. D40 cubic cm

   How do you know?
3. 3

   Warm restartWhat is the area of a parallelogram with base 9 in and height 4 in?

   1. A36 square in
   2. B13 square in
   3. C18 square in
   4. D26 square in

   How do you know?
4. 4

   Warm restartIn a parallelogram, how is the height measured?

   1. APerpendicular to the base
   2. BAlong the slanted side
   3. CAround the outside
   4. DFrom one corner to the opposite corner

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is the area of the triangular wall?

   1. A140 sq ft
   2. B280 sq ft
   3. C34 sq ft
   4. D70 sq ft

   Why is that the answer?
2. 6

   Think it throughHow many cans of paint does she need?

   1. A3
   2. B2
   3. C2.8
   4. D4

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhy round up instead of down?

   1. ABecause 2 cans cover only 100 sq ft, which is not enough for 140
   2. BBecause paint is always sold in threes
   3. CBecause 2.8 rounds to 3 by the usual rule
   4. DBecause the wall might be bigger

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelThe triangle fits inside a 12 × 8 rectangle. How does the triangle's area compare to the rectangle's area?

Use the words

Fill each blank with a word from the bank.

• The space inside a triangle, found with A = ½ × b × h, is the ___.
• The side of a triangle you measure the height from at a 90° angle is the ___.
• The perpendicular distance from the base to the opposite vertex is the ___.
• The amount of flat space inside a triangle is its ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Area of Triangles is forgetting the ½ — students multiply base × height like a rectangle and stop there, or they use the triangle's slanted side instead of the perpendicular height that's already given.
2. 10

   Say moreOn the grid your triangle (base 12, height 8) fits inside a 12 by 8 rectangle. Why do we divide by 2 to find the triangle's area?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: This is the firm's blueprint for a park. A rectangular plot is split by a diagonal path into two triangular garden beds that will be filled with soil.

   Show your work

Last check

These two come from Lesson 5.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A triangle has a base of 11 inches and a height of 8 inches. What is its area?

   1. A44 sq in
   2. B88 sq in
   3. C19 sq in
   4. D44 in

   Explain your choice.
2. 13

   From Lesson 5.1Explain your thinking — A parallelogram has a base of 13 inches and a height of 5 inches. What is its area?

   1. A65 sq in
   2. B36 sq in
   3. C18 sq in
   4. D65 in

   How do you know?
3. 14

   From Lesson 5.1Why use the height instead of the slanted side length?

   1. ABecause area needs the perpendicular distance between the two bases
   2. BBecause the slanted side is always longer
   3. CBecause parallelograms have no height
   4. DBecause the base is on the bottom

   How do you know?

Be honest — this tells your teacher what to do next