CEMC Banner

Problem of the Week

Problem C

Sentimental with Shapes

This year for Valentine’s Day you wish to send handmade greetings created using geometric shapes. You start by attaching two identical, white semi-circles to the hypotenuse of a white, isosceles right-angled triangle whose equal sides each measure \(\sqrt{32}\) cm. You then mount this new figure onto a rectangular piece of red construction paper as shown below. (The dashed line, the right angle symbol and the equal side measure markings will not be a part of the finished card.)

To complete your creation you write a personal message in red on the white region of the card.

Determine the total amount of area available in the white region for your special valentine sentiment.

The red rectangle with a white heart-shaped region in its interior. The top of the semi-circles touch the top edge of the rectangle, and the bottom vertex of the triangle touches the bottom edge of the rectangle. There is a right angle at this bottom vertex where the equal sides of the triangle meet. A dashed horizontal line marks the hypotenuse of the triangle.