MSTAR Practice Worksheet

Lesson 5-4: Apply Area Concepts to Solve Problems

Grade 6 Mathematics · Standard 6.GR.1

Name: Date:

These are MSTAR-style questions written for this curriculum to rehearse the format. They are not official Maryland assessment items. MSTAR — Maryland's new state test, first given in spring 2027 — uses the same kinds of questions you see here: selected response, select-all, two-part evidence questions, and written responses.

Part A — Skills Check

Warm up with the lesson's core skills — one best answer each.

Question 1Selected response · 1 point

An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?

A12 sq ft
B60 sq ft
C72 sq ft
D72 ft

Question 2Selected response · 1 point

A rectangular patio is 15 ft × 10 ft with a 5 ft × 4 ft rectangular flower bed cut out. What is the remaining area?

A20 sq ft
B130 sq ft
C150 sq ft
D170 sq ft

Question 3Selected response · 1 point

Find the area of an L-shape made of a 5×3 rectangle and a 2×4 rectangle.

A8 sq units
B15 sq units
C20 sq units
D23 sq units

Question 4Selected response · 1 point

When should you subtract areas instead of adding them to find the area of a composite figure?

AWhen the shapes overlap
BWhen one shape is larger than the other
CAlways subtract — never add
DWhen a piece is cut out or removed from a larger shape

Question 5Selected response · 1 point

A 7 ft by 5 ft rectangle has a triangle (base 7 ft, height 4 ft) on top. Add the two areas. What is the total area?

A14 sq ft
B35 sq ft
C49 sq ft
D63 sq ft

Question 6Selected response · 1 point

Plan 2 — L-shaped lobby: decompose the L into two rectangles, one 9 ft by 6 ft and one 7 ft by 3 ft, then ADD. What is the total floor area?

A21 sq ft
B54 sq ft
C63 sq ft
D75 sq ft

Part B — Test-Format Questions

These match the state test's formats: two-part questions, select-all, and written responses.

Question 7Two-part question

Part A

An L-shaped room splits into two rectangles: one is 12 feet by 8 feet, the other is 6 feet by 5 feet. What is the total floor area?

Fill in the bubble next to the one best answer.

A30 square feet
B62 square feet
C96 square feet
D126 square feet

Part B

Answer Part A before Part B — Part B asks about your reasoning.

Why is decomposing a composite figure into rectangles a valid strategy?

AThe areas of the non-overlapping pieces add to the area of the whole figure.
BRectangles are the only shapes with area.
CAny shape can be turned into one large rectangle.
DThe perimeter stays the same after decomposing.

Question 8Written response · 2 points

Type II Reasoning: Counting a Region Twice

Nia split a composite figure into a 10 by 4 rectangle and a triangle with base 10 and height 4. She added 40 + 20 = 60 square units — but the triangle sat ON TOP of part of the rectangle she had already counted.

Explain the error in Nia's method and state what she must check before adding areas.

Write your answer in complete sentences. Show or explain your mathematical thinking.

Part C — Show Your Thinking

Answer in writing, the way the state test's constructed responses work.

Question 9Written response · 2 points

A T-shaped room can be decomposed in two different ways. Show both ways and prove they give the same total area. Use a T-shape where the top is 14 ft × 4 ft and the stem is 6 ft × 10 ft.

Write your answer in complete sentences. Show or explain your mathematical thinking.