Question

Math 6B Unit 6
Use Area to Solve Problems Portfolio
To earn full credit:
Show/Explain your thoughts on how you solved the problems by showing your work to receive full credit.
Please write/type your Full Name:
Nikolai Matthews
STAAR Reference Chart Link
Question #1 (1 point)
The dimensions of a rectangular prism are shown. What is the volume of the rectangular prism in cubic inches?
2.7 in
5 in 7 in
Question #2 (1 point)
What is the area of the parallelogram in square centimeters?
Remember

8 cm
5.5 cm
12 cm
___________ cm2
that the
height
creates a
right angle with the base of the shape.

Question #3 (1 point)
What is the area of the trapezoid in square feet? 32 ft
44 ft
40 ft
52 ft
___________ ft2

Remember that the
height
creates a
right angle with the base of the shape.

Question #4 (1 point) Hint: Start

What is the missing angle measurement of a triangle with two angle measures of 35° and 84° ?
with recalling how many
degrees there are in a
triangle.
Question #5 (1 point)
Based on the lengths of the sides, which angle is the largest? X
Hint: Angles and their
opposite
sides have a direct

3.4 cm
6.5 cm
relationship.

YZ 9.8 cm
X
Y
Z

Question #6 (2 points total)
In Triangle QRT, angle Q measures 80° and angle T measures 35°.
Which list shows the side lengths of the triangle in order from greatest to least?
Use the Hints to Draw your Triangle to show your work for 1 point.
Hints:
1. Recall the total number of degrees

A B C D
QT RT QR RT QT QR QT QR RT RT QR QT
in a triangle.
2. Draw your own triangle.
3. Find the missing angle’s degree.
4. Label each angle. 5. Recall how the angles and their opposite sides
have a direct
relationship to
each other.

Question #7 (2 points)
A right rectangular prism with a square base is shown. Dimensions are given in units.
The volume of the prism is 192 cubic units. What is the height, h, of the prism in units?
Don’t forget to show how you solved this problem.
A key piece of
information is provided in the first sentence:
Square Base
What information do you now know based on this information?

A B C D
48 units 12 units 24 units 64 units
h

4

Question #8 (2 points)
John is drawing a right triangle PQR on the coordinate grid. The base of the triangle is shown.
The height of the triangle is 5 units. Which ordered pair could represent point R?
Be sure to show how
you solve this problem.

Hint:
1. Plot each point listed in the
answers.
A
(4, -2)
B
(1, 4)
(6, -1)
C
(-2, 5)P Q D
2. Which point creates a
height of 5
units?

Question #9 (1 point)
Which inequality is true when ���� = ����?

A B C D
40���� > 320 40���� < 320 40���� < −320 40���� ≤ 320
Hint:
1. Review the symbols for greater than, less than and equal to.
2. Solve each problem in the answers to find
out which inequality is true.

Questions #10 – 13 (1 point each)Work each problem

Use the chart to answer the next 4 questions. Type your answers in the boxes.
Find the Missing Measurements
by finding the Area for each shape
Question Number
Figure
Base
length
Height
Area
10
Triangle
2.5 m
14 m


11
Triangle
10 in


25 in2
12
Rectangle
17 cm
11 cm


13
Parallelogram
412ft


99 ft2



separately to find either
the height or the area of
each shape.

Answer 1

Full Name: Nikolai Matthews

Work shown for each question below.

Question 1 (1 pt)
Dimensions: 2.7 in, 5 in, 7 in
Volume = length × width × height = 2.7 × 5 × 7 = 2.7 × 35 = 94.5
Answer: 94.5 in³

Question 2 (1 pt)
Parallelogram: base = 12 cm, height = 5.5 cm (height is perpendicular to base)
Area = base × height = 12 × 5.5 = 66
Answer: 66 cm²

Question 3 (1 pt)
(Using the two parallel sides as the bases 40 ft and 52 ft, and the height marked 32 ft.)
Area of trapezoid = (base1 + base2)/2 × height = (40 + 52)/2 × 32 = 92/2 × 32 = 46 × 32 = 1472
Answer: 1472 ft²
(Note: I used 40 ft and 52 ft as the bases and 32 ft as the height as indicated by the diagram labeling.)

Question 4 (1 pt)
Triangle angles: 35° and 84°
Sum of triangle angles = 180° → missing angle = 180 − (35 + 84) = 180 − 119 = 61°
Answer: 61°

Question 5 (1 pt)
Sides given: YZ = 9.8 cm (this side is opposite angle X), other sides 6.5 cm and 3.4 cm
Largest side = 9.8 cm so largest angle is opposite it → angle X is largest.
Answer: ∠X

Question 6 (2 pts)
Triangle QRT: ∠Q = 80°, ∠T = 35°
Missing ∠R = 180 − (80 + 35) = 180 − 115 = 65°
Order sides from greatest to least by comparing opposite angles:
Largest angle: ∠Q = 80° → opposite side = RT
Next: ∠R = 65° → opposite side = QT
Smallest: ∠T = 35° → opposite side = QR
Order greatest to least: RT, QT, QR
Answer: RT, QT, QR (choice B)

Question 7 (2 pts)
Square base side = 4 units (given). Volume = 192 units³.
Base area = 4² = 16. Volume = base area × height → 16 × h = 192 → h = 192/16 = 12
Answer: 12 units

Question 8 (2 pts)
Base of triangle shown on the grid has y = −1 (from the diagram). Height must be 5 units perpendicular to that base, so R must have y = −1 + 5 = 4.
Plot the answer choices: only (1, 4) has y = 4.
Check vertical distance: |4 − (−1)| = 5 → correct.
Answer: (1, 4)

Question 9 (1 pt)
Given 40m = 320 → substitute m = 8. Evaluate inequalities:
A: 40m > 320 → 320 > 320 (false)
B: 40m < 320 → 320 < 320 (false)
C: 40m < −320 → 320 < −320 (false)
D: 40m ≤ 320 → 320 ≤ 320 (true)
Answer: D

Questions 10–13 (1 pt each) — find missing measures using area formulas

Question 10
Triangle: base = 2.5 m, height = 14 m
Area = 1/2 × base × height = 1/2 × 2.5 × 14 = 17.5
Answer (Area): 17.5 m²

Question 11
Triangle: base = 10 in, Area = 25 in²
Area = 1/2 × base × height → 25 = 1/2 × 10 × h = 5h → h = 25/5 = 5
Answer (Height): 5 in

Question 12
Rectangle: length = 17 cm, width = 11 cm
Area = length × width = 17 × 11 = 187
Answer (Area): 187 cm²

Question 13
Parallelogram: base = 412 ft, Area = 99 ft² (find height)
Area = base × height → 99 = 412 × h → h = 99/412 ft ≈ 0.240 ft
Answer (Height): 99/412 ft (≈ 0.240 ft)

End of work.