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Quizzes > High School Quizzes > Mathematics

Find the Shaded Area Practice Quiz

Solve problems with detailed answer explanations

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art for trivia on The Shaded Area Challenge quiz testing high school geometry skills.

A rectangle with a length of 10 cm and a width of 5 cm is divided into two equal regions. If one region is shaded, what is the area of the shaded region?
25 cm²
50 cm²
10 cm²
5 cm²
The area of the rectangle is 10*5 = 50 cm². Dividing it into two equal regions means each region has an area of 25 cm². This calculation confirms that 25 cm² is the correct answer.
A square with a side length of 6 cm has a smaller square of side 2 cm removed from one of its corners. What is the area of the remaining shaded region?
32 cm²
34 cm²
30 cm²
28 cm²
The full square has an area of 6² = 36 cm², and the removed square has an area of 2² = 4 cm². Subtracting the removed area from the whole gives 36 - 4 = 32 cm², which is the area of the remaining shaded region.
In a circle with a radius of 4 cm, if a quarter of the circle is shaded, what is the area of the shaded region? (Use π for exact value)
4π cm²
8π cm²
12π cm²
16π cm²
The entire circle has an area of π*(4²) = 16π cm². A quarter of that area is 16π/4 = 4π cm², making it the correct answer.
A triangle with a base of 8 cm and a height of 5 cm is divided into two congruent regions. What is the area of one shaded region?
10 cm²
20 cm²
15 cm²
5 cm²
The area of the triangle is ½ × 8 × 5 = 20 cm². Dividing the triangle into two equal regions gives each area as 20/2 = 10 cm², which confirms the correct answer.
A composite figure consists of a 4 cm by 6 cm rectangle with an 8 cm² rectangle removed, leaving an L-shaped shaded region. What is the area of the shaded region?
16 cm²
24 cm²
8 cm²
18 cm²
The area of the full rectangle is 4 × 6 = 24 cm². After removing an area of 8 cm², the remaining shaded region has an area of 24 - 8 = 16 cm².
A large rectangle measuring 12 cm by 8 cm has a smaller rectangle of 4 cm by 3 cm cut out from its interior. What is the area of the remaining shaded region?
84 cm²
90 cm²
72 cm²
96 cm²
The larger rectangle has an area of 12 × 8 = 96 cm². The area of the cut-out rectangle is 4 × 3 = 12 cm², so the remaining shaded area is 96 - 12 = 84 cm².
A circle with a radius of 7 cm has a 60° sector shaded. What is the area of the shaded sector?
49π/6 cm²
49π/3 cm²
49π/12 cm²
7π/6 cm²
The full circle has an area of π × 7² = 49π cm². Since 60° is 1/6 of 360°, the shaded sector's area is 49π/6 cm².
A square with a side length of 10 cm has a circle inscribed inside it. What is the area of the shaded region between the square and the circle?
100 - 25π cm²
100 - 10π cm²
25π - 100 cm²
100 + 25π cm²
The area of the square is 10² = 100 cm², and the inscribed circle has a radius of 5 cm with an area of π × 5² = 25π cm². Subtracting the circle's area from the square's area gives 100 - 25π cm².
Two overlapping rectangles each have an area of 24 cm², with an overlapping area of 6 cm². What is the total area of the shaded (combined) region?
42 cm²
48 cm²
36 cm²
30 cm²
The combined area of the two rectangles is 24 + 24 = 48 cm², but the overlapping area of 6 cm² is counted twice. Subtracting it once gives 48 - 6 = 42 cm².
A semicircular region with a radius of 10 cm is attached to a rectangle measuring 10 cm by 6 cm. If only the semicircular part is shaded, what is the area of the shaded region?
50π cm²
100π cm²
25π cm²
60π cm²
The area of a full circle with a radius of 10 cm is π × 10² = 100π cm². Since the region is a semicircle, its area is half of that, which is 50π cm².
Find the area of a shaded annulus (ring) formed by two concentric circles, where the outer circle has a radius of 7 cm and the inner circle has a radius of 4 cm.
33π cm²
11π cm²
53π cm²
25π cm²
Subtracting the area of the inner circle (π × 4² = 16π cm²) from the outer circle (π × 7² = 49π cm²) gives an annulus area of 49π - 16π = 33π cm².
A square with a side length of 8 cm has a quarter circle removed from one corner. What is the area of the remaining shaded region?
64 - 16π cm²
64 - 8π cm²
16π - 64 cm²
64 + 16π cm²
The square has an area of 8² = 64 cm², and the removed quarter circle has an area of ¼ × π × 8² = 16π cm². Therefore, the remaining shaded area is 64 - 16π cm².
A rectangle with an area of 60 cm² is divided by drawing a diagonal. If one of the resulting triangles is shaded, what is its area?
30 cm²
60 cm²
15 cm²
45 cm²
Dividing the rectangle along its diagonal creates two congruent triangles. Each triangle has an area equal to half of 60 cm², which is 30 cm².
A composite figure consists of a rectangle with an area of 72 cm² and a semicircular cut-out from one side, where the semicircle's diameter is 6 cm. What is the area of the remaining shaded region?
72 - 4.5π cm²
72 - 9π cm²
72 + 4.5π cm²
72 - 6π cm²
First, find the area of the semicircular cut-out using a radius of 3 cm, which is (1/2) × π × 3² = 4.5π cm². Subtracting this from the rectangle's area gives 72 - 4.5π cm².
A circle with an area of 64π cm² has a 90° sector removed. What is the area of the remaining shaded region?
48π cm²
64π cm²
16π cm²
32π cm²
A 90° sector represents one-fourth of the circle's area, which is 64π/4 = 16π cm². Subtracting this from the total area of 64π cm² leaves 48π cm² for the shaded region.
Two identical circles with a radius of 4 cm intersect such that the overlapping unshaded region has an area of 6 cm². What is the total area of the shaded regions (areas of both circles excluding the overlap)?
32π - 6 cm²
32π + 6 cm²
16π - 6 cm²
16π + 6 cm²
Each circle has an area of π × 4² = 16π cm², so together they sum to 32π cm². Since the overlapping area of 6 cm² is unshaded and would be counted twice, subtract it once to yield 32π - 6 cm².
A composite figure consists of three shapes: a rectangle with an area of 24 cm², a triangle with an area of 12 cm², and a semicircle with an area of 8π cm². If only the rectangle and triangle are shaded, what is the area of the shaded region?
36 cm²
24 cm²
12 cm²
36 - 8π cm²
Since only the rectangle (24 cm²) and the triangle (12 cm²) are shaded, their areas add up to 24 + 12 = 36 cm². The semicircle is not included in the shaded portion.
A circle with a radius of 6 cm has a chord that creates a segment with a central angle of 120°. Using the formula for a circular segment, what is the approximate area of this shaded segment? (Use sin 120° ≈ 0.866)
Approximately 22.11 cm²
Approximately 15.59 cm²
Approximately 37.70 cm²
Approximately 30.00 cm²
The area of the sector is (120/360) × π × 6² = 12π (about 37.70 cm²), and the area of the triangle is 0.5 × 6² × sin 120° ≈ 15.59 cm². Subtracting the triangle's area from the sector's area gives approximately 22.11 cm².
A composite shape is made by adjoining a rectangle with an area of 40 cm² and a half-circle with an area of 18π cm² along one side. If the overlapping area where the shapes connect is 10 cm² and is counted in both shapes, what is the total area of the shaded region?
30 + 18π cm²
40 + 18π cm²
30 + 10π cm²
40 - 18π cm²
By adding the areas of the rectangle and half-circle, we get 40 + 18π. However, the overlapping area of 10 cm² is counted twice, so subtract it once to obtain 40 + 18π - 10 = 30 + 18π cm².
A design features a regular hexagon with an area of 60√3 cm² and an inscribed circle with an area of 20π cm². What is the area of the shaded region between the hexagon and the circle?
60√3 - 20π cm²
60√3 + 20π cm²
20π - 60√3 cm²
60√3 cm²
The shaded region is determined by subtracting the area of the inscribed circle from the area of the hexagon, which results in 60√3 - 20π cm².
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Study Outcomes

  1. Identify key geometric shapes and components within composite figures.
  2. Calculate areas of basic shapes such as triangles, rectangles, and circles.
  3. Analyze composite figures to determine the area of shaded regions.
  4. Apply appropriate formulas to compute areas and solve for missing dimensions.
  5. Evaluate problem-solving approaches to verify the accuracy of calculated areas.

Free: Find Area of Shaded Region Answers Cheat Sheet

  1. Master basic area formulas - Learn A = length × width for rectangles, A = ½ × base × height for triangles, and A = π × radius² for circles by sketching fun shapes. These building blocks are your go‑to tools for any flat figure. HighLine Math: Area Formulas
  2. Composite figure breakdown - Break complex shapes into simpler pieces like rectangles, triangles, and semicircles, then sum their areas. Treat it like solving a puzzle where each piece fits perfectly. Online Math Learning: Shaded Areas
  3. Shoelace Theorem wizardry - Use coordinates of a polygon's vertices to compute its area with a neat sum‑and‑subtract trick. Once you list out points, the shoelace formula feels like magic math. Wikipedia: Shoelace Formula
  4. Shaded region subtraction - Practice taking the total area and subtracting unshaded parts - think of cutting away the crust to reveal the pizza's cheesy center. This strategy makes shading challenges a breeze. Online Math Learning: Shaded Areas
  5. Parallelograms & trapezoids - Get comfy with A = base × height for parallelograms and A = ½ × (base₝ + base₂) × height for trapezoids. Imagine stretching or stacking rectangles to see why these formulas work. HighLine Math: Area Formulas
  6. Regular polygon hack - Use A = ½ × perimeter × apothem to tackle any regular polygon by splitting it into identical triangles. Visualize slicing a pizza into equal wedges and adding them back up. HighLine Math: Area Formulas
  7. Lateral & total surface areas - Explore cylinders, cones, and prisms by unfolding nets into flat shapes. Sum side areas for lateral surface and add caps for total surface to become a 3D area pro. BYJU'S: Surface Area Formulas
  8. Word problem workouts - Apply area formulas in real‑life contexts like garden layouts or room designs. Turning everyday scenarios into math puzzles levels up your critical thinking. Online Math4All: Word Problems
  9. Flashcard active recall - Quiz yourself with colorful cards to lock in each formula; active recall is your memory's best friend. Flashcards transform rote memorization into a game. Quizlet: Area Formulas Flashcards
  10. Review & repeat - Cycle through problems daily, track your progress, and celebrate small wins. Consistent practice cements concepts and boosts your geometry confidence. Online Math Learning: Shaded Areas
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