Unit 1, Lesson 6
Area of Parallelograms
Grade 6
Practice
Problem 1
Which three of these parallelograms have the same area as each other?
Four parallelograms, labeled A, B, C, and D. Figure A, the top and bottom sides each 5 units, slanted sides descend 3 units and move right 1 unit. Figure B, the top and bottom sides are each 3 units, slanted sides ascend 5 units while moving right 6 units. Figure C is a square of 4 units on each side. Figure D, the left and right sides are each 3 units, and the top and bottom sides descend 1 unit as they move right 5 units.
A
B
C
D
Problem 3
Here are the areas of three parallelograms. Use them to find the missing length (labeled with a "?") on each parallelogram.
A: 10 square units
Parallelogram A, right side = 5 units, height = question mark.
B: 21 square units
Parallelogram B, bottom side = question mark. Right triangle drawn outside of parallelogram, base = 1 unit, height = 7 units.
C: 25 square units
Parallelogram C, bottom side = question mark. Right triangle drawn outside of parallelogram, base = 2.5 units, height = 5 units.
Problem 4
The Dockland Building in Hamburg, Germany is shaped like a parallelogram.
If the length of the building is 86 meters and its height is 55 meters, what is the area of this face of the building?
Problem 5
Select all segments that could represent a corresponding height if the side \(m\) is the base.
e
f
g
h
j
k
Problem 6
Find the area of the shaded region. All measurements are in centimeters. Show your reasoning.
A shaded rectangle located at an angle within a larger rectangle. The sides of the larger rectangle are divided where the smaller rectangle contacts them. The longer sides are labeled 2 and 12 on each side of the divide, and the shorter sides are labeled 6 and 4 on each side of the divide.