Name: _________________________________ Date: COVERING AND SURROUNDING STUDY GUIDE GRADE 6 Investigation 2: Measuring Triangles (Digits: Homework Helper v2 p.432-­‐438, 444-­‐450) •
•
•
•
A polygon is ___________________________________________________. Two lines that form a right angle are __________________________ lines. A vertex of a polygon is where two sides of the polygon meet. Triangles often seem to rest on one side. This side is usually called the base. Any of the triangle’s three sides can serve as the _________. The ___________ of a triangle is the perpendicular distance from the vertex opposite the base to the base. TRY THIS: Label the triangles “base” and “height” height base 1
The formula for finding the area of a triangle is A = b x h. Here, b is the base and h is the height. 2
The area of a triangle and the area of a rectangle are related. To solve for both areas you multiply by base 1
and height, except for a triangle is of a rectangle. 2
height
3cm
1
height
A = b x h 2
3cm
1
A = (6 x 3) Base = 6cm
2
cm
1
2
base
A = (18) A = 9 cm 2
6cm
TRY THIS: Find the area of the triangle. 1
8 in. 2
4 in.
6 in.
6 in.
Schnitzer.2015 1 Investigation 3: Measuring Parallelograms (Digits: Homework Helper v2 p.439-­‐443, 451-­‐463) •
•
•
When working with rectangles, you use the measurements length and width. For triangles, you use the side lengths, the base, and the height. Like triangles, parallelograms are often described by side length, base, and height. The formula for the area of a parallelogram is A = b x h, where A is the area, b is the base, and h is the height. Using two previous formulas you have learned, the area of a triangle and a rectangle, you can discover how the formula was derived. Here a student knows about the area of a Here a student knows the area of a rectangle triangle to find the area of any parallelogram. to find the area of a parallelogram. She makes He draws a diagonal and a height on the a drawing to show how she cut a triangle off parallelogram and uses the formula for finding one side of the parallelogram and added it to the area of a triangle. the other side. TRY THIS: Find the area of the parallelogram. 6 in.
8 in.
12 in.
Investigation 4: Measuring Surface Area and Volume (Digits: Homework Helper v2 p.464-­‐507) • A net is a _____________________________________________________________________ _____________________________________________________________________________. Schnitzer.2015 2 •
The surface area of a box is the total area of all its faces. •
A _________ is a three-­‐dimensional shape with two parallel and congruent faces called ________. The other faces are called lateral (side) faces. •
A ________________________ has bases that are rectangles. The length and width of a rectangular prism are the length and width of its rectangular base. The height is the distance from the bottom of the prism to its top. The length, width, and height of a rectangular prism are its dimensions. To find the surface area of a figure, find the area of all the faces of the prism. Then add up the totals. For the rectangular prism to the left the surface area would be 88cm2. 8cm2 + 24cm2 + 12cm2 + 24cm2 + 12cm2 + 8cm2 = 88 cm2 •
The volume of a box is the number of unit cubes that it would take to fill the box. We can find the volume of a rectangular prism by multiplying the length by the width by the height. TRY THESE: Find the surface area of the figure below. Find the volume of the figure below. Schnitzer.2015 3