第9章数学モデルと幾何

A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides $250$ feet long, and the triangles are isosceles right triangles. Find the area of the park.

A gift box will be made from a rectangular piece of cardboard measuring $12$ inches by $20$ inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are $3$ inches. Find the area of the cardboard after the corners are cut out.

Perry needs to put in a new lawn. His lot is a rectangle with a length of $120$ feet and a width of $100$ feet. The house is rectangular and measures $50$ feet by $40$ feet. His driveway is rectangular and measures $20$ feet by $30$ feet, as shown. Find the area of Perry’s lawn.

Denise is planning to put a deck in her back yard. The deck will be a $\text{20-ft}$ by $\text{12-ft}$ rectangle with a semicircle of diameter $6$ feet, as shown below. Find the area of the deck.

Area of a Tabletop Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a $\text{1-ft}$ by $\text{3-ft}$ rectangle with a semicircle at each end, as shown. ⓐ Find the area of the table with one leaf up. ⓑ Find the area of the table with both leaves up.

Painting Leora wants to paint the nursery in her house. The nursery is an $\text{8-ft}$ by $\text{10-ft}$ rectangle, and the ceiling is $8$ feet tall. There is a $\text{3-ft}$ by $\text{6.5-ft}$ door on one wall, a $\text{3-ft}$ by $\text{6.5-ft}$ closet door on another wall, and one $\text{4-ft}$ by $\text{3.5-ft}$ window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?

Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.

A circle has a diameter of $14$ feet. Find the area of the circle ⓐ using $3.14$ for$\pi$ ⓑ using $\frac{22}{7}$ for $\text{π}.$ ⓒ Which calculation to do prefer? Why?