Interactive multiple-choice quiz: اختبار الرياضيات الصف السادس الوحدة الثامنة
استكشاف الهندسة: حساب مساحات المضلعات
يركز هذا الاختبار على المبادئ الأساسية للهندسة في حساب مساحات الأشكال المختلفة مثل متوازي الأضلاع، المثلث، وشبه المنحرف. يتعلم الطلاب كيفية تطبيق القواعد الرياضية لإيجاد المساحة من خلال المعطيات المعطاة، وكيفية التعامل مع المضلعات المنتظمة كالسداسي والثماني عن طريق تقسيمها إلى مثلثات بسيطة. تشمل المسائل تطبيقات حياتية مثل حساب تكاليف فرش الأرضيات أو مقارنة تكاليف الإيجار بناءً على المساحة، مما يعزز مهارات التفكير المنطقي والحل الرياضي الدقيق لدى طلاب الصف السادس.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
What is the formula for calculating the area (A) of a parallelogram with base (b) and height (h)?
Explanation
The area of a parallelogram is calculated by multiplying the length of the base by the height.
Question 2
DB ID: 3001
Points: 1
If a parallelogram has a base of 10 cm and a height of 5 cm, what is its area?
Explanation
Using the formula Area = base × height, we get 10 cm × 5 cm = 50 cm².
Question 3
DB ID: 3002
Points: 1
In the flag of the Republic of the Congo, what is the area of the yellow region?
Explanation
The yellow region is shown as a parallelogram with a base of 6.8 in and a height of 2 in. Area = 6.8 × 2 = 13.6 in².
Question 4
DB ID: 3003
Points: 1
What is the mathematical relationship between the area of a triangle and a parallelogram with the same base and height?
Explanation
The formula for the area of a triangle is \(\frac{1}{2}bh\), while for a parallelogram it is bh. Thus, the triangle's area is half that of the parallelogram.
Question 5
DB ID: 3004
Points: 1
Calculate the area of a triangle with a base of 12cm and a height of 5cm.
Explanation
Area = \(\frac{1}{2} \times base \times height = \frac{1}{2} \times 12 \times 5 = 30\) cm².
Question 6
DB ID: 3005
Points: 1
Norma has an A-frame cabin. The back of the cabin is a triangle with a base of 8yd and a height of 5yd. If the windows and doors cover 3.5yd², how much area is left to be painted?
Explanation
Total triangular area = \(\frac{1}{2} \times 8 \times 5 = 20\) yd². Subtracting windows and doors: 20 - 3.5 = 16.5 yd².
Question 7
DB ID: 3006
Points: 1
Which of the following is the correct formula for the area (A) of a trapezoid with bases b1, b2 and height h?
Explanation
The area of a trapezoid is defined as half the product of its height and the sum of its parallel bases.
Question 8
DB ID: 3007
Points: 1
Calculate the area of a trapezoid with bases of 7m and 9m, and a height of 4m.
Explanation
Area = \(\frac{1}{2} \times 4 \times (7 + 9) = 2 \times 16 = 32\) m².
Question 9
DB ID: 3008
Points: 1
The shape of Arkansas resembles a trapezoid with parallel bases of 475km and 300km, and a height of 400km. What is the approximate area of Arkansas?
Explanation
Using the trapezoid area formula: \(\frac{1}{2} \times 400 \times (475 + 300) = 200 \times 775 = 155,000\) km².
Question 10
DB ID: 3009
Points: 1
If a regular hexagon is divided into triangles from its center, how many triangles will be formed?
Explanation
A hexagon has 6 sides; connecting each vertex to the center forms 6 congruent triangles.
Question 11
DB ID: 3010
Points: 1
Kendra knitted a coaster shaped like a regular hexagon. Each side of the hexagon is 3.5in and the height of each internal triangle is 3.03in. What is the total area of the coaster? (Round to the nearest hundredth)
Explanation
The hexagon consists of 6 triangles. Area = \(6 \times (\frac{1}{2} \times 3.5 \times 3.03) = 6 \times 5.3025 = 31.815\) in², which rounds to 31.82 in².
Question 12
DB ID: 3011
Points: 1
Julian is building a picnic table with an octagon-shaped top. Each side of the octagon is 2.5ft and the height of the internal triangle is 3.02ft. If the wood costs 3.95$ per square foot, what is the total cost for the top of the table?
Explanation
Total area of octagon = \(8 \times (\frac{1}{2} \times 2.5 \times 3.02) = 30.2\) ft². Total cost = 30.2 × 3.95 = 119.29$.
Question 13
DB ID: 3012
Points: 1
Ethan is comparing two rental spaces for his new pet store. Space A is a rectangle with an area of 320ft² and costs 14.75$ ft². Space B is a trapezoid with an area of 328ft² and costs 14.50$ ft². Which location has the lower total monthly rental price?
Explanation
Cost of Space A = 320 × 14.75 = 4,720$. Cost of Space B = \(328 \times 14.50 = 4,756\)$. Space A has the lower price.
Question 14
DB ID: 3013
Points: 1
The shape of the park resembles a trapezoid. Which of the following is the approximate area of the park?
Explanation
Using dimensions from the image (bases 480 and 338, height 378): Area = \(\frac{1}{2} \times 378 \times (480 + 338) = 189 \times 818 = 154,602\).
Question 15
DB ID: 3014
Points: 1
Kim wants to replace the area covered by this rug with hardwood flooring. The rug is shaped like a regular octagon with 3-foot sides.
Explanation
The image shows the height (apothem) of an internal triangle is 3.6 ft. Total area = \(8 \times (\frac{1}{2} \times 3 \times 3.6) = 4 \times 10.8 = 43.2\) ft².
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