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Problem of the Week

Problem C

A Homemade Expression of Love

Maggie wants to make a special card for Valentine’s Day. She starts with a square piece of red paper with a side length of \(12\mbox{ cm}\). She then pastes two white semi-circles, each with radius \(3\mbox{ cm}\), and a white triangle onto the square sheet of red paper, as shown below. (The dashed line and the right angle symbols will not actually be on the finished card.).

She is going to write her valentine a message in red ink on the white region of the card.

Determine the total amount of area available in the white region for Maggie’s special valentine greeting.

A red square with a white heart-shaped region in its interior. A dashed horizontal line runs the width of the heart which is the same as the width of the square. The line decomposes the heart into two semi-circles lying side by side and a triangle. The top of the semi-circles touch the top edge of the square, and the bottom vertex of the triangle touches the middle of the bottom edge of the square.

Theme: Geometry