Exploring Geometry: Shapes and Properties

Identify the shape that has four equal sides and four right angles.

• Triangle

• Rectangle

• Square

• Circle

Answer explanation

A square is defined as a shape with four equal sides and four right angles. While a rectangle has four right angles, it does not require equal sides. Therefore, the correct answer is a square.

Tags

CCSS.5.G.B.4

Which shape is classified as a polygon?

• Circle

• Triangle

• Sphere

• Cylinder

Answer explanation

A polygon is a closed figure with straight sides. Among the options, a triangle is the only shape that fits this definition, as it has three straight sides. A circle, sphere, and cylinder do not have straight sides.

Tags

CCSS.2.G.A.1

Calculate the perimeter of a rectangle with a length of 8 cm and a width of 3 cm.

• 11 cm

• 22 cm

• 24 cm

• 16 cm

Answer explanation

To calculate the perimeter of a rectangle, use the formula P = 2(length + width). Here, P = 2(8 cm + 3 cm) = 2(11 cm) = 22 cm. Thus, the correct answer is 22 cm.

Tags

CCSS.4.MD.A.3

What is the area of a square with a side length of 5 cm?

• 10 cm²

• 15 cm²

• 20 cm²

• 25 cm²

Answer explanation

The area of a square is calculated by squaring the side length. Here, the side length is 5 cm. Therefore, the area = 5 cm × 5 cm = 25 cm². Thus, the correct answer is 25 cm².

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Which of the following shapes has exactly one line of symmetry?

• Circle

• Rectangle

• Isosceles triangle

• Scalene triangle

Answer explanation

An isosceles triangle has one line of symmetry that divides it into two equal halves. In contrast, a circle has infinite lines of symmetry, a rectangle has two, and a scalene triangle has none.

Tags

CCSS.4.G.A.3

Draw a rectangle with a length of 6 cm and a width of 4 cm. Which of the following statements is true about the shape you drew?

• It has four lines of symmetry.

• It has two lines of symmetry.

• It has no lines of symmetry.

• It has one line of symmetry.

Answer explanation

A rectangle has two lines of symmetry: one vertical and one horizontal. This means it can be folded along these lines and both halves will match perfectly, confirming that the correct choice is 'It has two lines of symmetry.'

Tags

CCSS.4.G.A.3

A triangle has sides of lengths 3 cm, 4 cm, and 5 cm. What type of triangle is this?

• Equilateral

• Isosceles

• Scalene

• Right-angled

Answer explanation

The triangle with sides 3 cm, 4 cm, and 5 cm is a right-angled triangle because it satisfies the Pythagorean theorem: 3² + 4² = 5² (9 + 16 = 25). Thus, the correct answer is 'Right-angled'.

Tags

CCSS.4.G.A.2

Calculate the area of a triangle with a base of 10 cm and a height of 6 cm.

• 30 cm²

• 60 cm²

• 40 cm²

• 20 cm²

Answer explanation

The area of a triangle is calculated using the formula: Area = 1/2 × base × height. Here, Area = 1/2 × 10 cm × 6 cm = 30 cm². Therefore, the correct answer is 30 cm².

Tags

CCSS.6.G.A.1

Which shape has rotational symmetry of order 4?

• Square

• Rectangle

• Triangle

• Pentagon

Answer explanation

A square has rotational symmetry of order 4 because it can be rotated at 90-degree intervals (0°, 90°, 180°, 270°) and still look the same. Other shapes listed do not have this level of symmetry.

Tags

CCSS.HSG.CO.A.4

• 21.98 cm

• 43.96 cm

• 14 cm

• 28 cm

Answer explanation

To find the circumference of a circle, use the formula C = 2πr. Here, r = 7 cm. Thus, C = 2 × 3.14 × 7 = 43.96 cm. Therefore, the correct answer is 43.96 cm.

Tags

CCSS.7.G.B.4