Question

an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. the heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the legnth of the shorter base of each trapezoid is 1.5 centimeters. what is the total area of the face of the watch to the nearest tenth of a square centimemter?

Answer 1

The total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²

Since an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. The heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the length of the shorter base of each trapezoid is 1.5 centimeters, the radii of the hexagon, and the base of the trapezoid form a triangle of

• height, h = apothem of the hexagon = 2 cm and
• base, b = length of shorter base of trapezoid.

Area of the triangle

So, the area of this triangle is A = 1/2bh

= 1/2 × 1. 5 cm × 2 cm

= 1.5 cm × 1 cm

= 1.5 cm²

Area of the hexagon

Since there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A

= 6 × 1.5 cm²

= 9.0 cm²

So, the total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²

Learn more about area of a hexagon here:

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