Geometric Shapes and Mensuration Flashcards

What is the sum of the interior angles of a pentagon?

Answer: 540°

Sum = (n − 2) × 180° = (5 − 2) × 180° = 3 × 180° = 540°.

The interior angle of a regular polygon is 120°. How many sides does it have?

Answer: 6

Exterior angle = 180° − 120° = 60°; number of sides = 360° ÷ 60° = 6.

A right-angled triangle has legs of 6 cm and 8 cm. What is the length of the hypotenuse?

Answer: 10 cm

By the Pythagorean theorem: hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

What is the sum of the exterior angles of any convex polygon?

Answer: 360°

The sum of exterior angles of any convex polygon is always 360°, regardless of the number of sides.

What is the area of a composite shape formed by a rectangle 8 cm × 5 cm joined to a right triangle with base 5 cm and height 3 cm?

Answer: 47.5 cm²

Rectangle area = 40 cm²; triangle area = ½ × 5 × 3 = 7.5 cm²; total = 47.5 cm².

How many lines of symmetry does a regular hexagon have?

Answer: 6

A regular hexagon has 6 lines of symmetry — 3 through opposite vertices and 3 through midpoints of opposite sides.

What is the area of a rhombus whose diagonals measure 12 cm and 8 cm?

Answer: 48 cm²

Area of a rhombus = (d₁ × d₂) ÷ 2 = (12 × 8) ÷ 2 = 96 ÷ 2 = 48 cm².