L2 · Area of triangles and other polygons

1. 1.

   Find the area of the triangle.

   Answer. 55 square ft

   A = 12 × b × h = 12 × 11 × 10 = 55 square ft.

2. 2.

   Find the area of the trapezoid.

   Answer. 19.5 square cm

   A = 12(b₁ + b₂)h = 12(4 + 9)(3) = 19.5 square cm.

3. 3.

   A polygon is a 11-by-6 rectangle joined to a 4-by-5 rectangle. Find the total area.

   Answer. 86 square ft

   11 × 6 = 66, 4 × 5 = 20, total 86 square ft.

4. 4.

   Find the area of the triangle.

   Answer. 54 square in

   A = 12 × b × h = 12 × 12 × 9 = 54 square in.

5. 5.

   Theo tiles a patio that is a trapezoid with bases 8 cm and 16 cm and height 5 cm. What area of tile is needed?

   Answer. 60 square cm

   A = 12(8 + 16)(5) = 60 square cm.

6. 6.

   Malik’s classroom floor is an L-shape: a 8-by-5 in rectangle joined to a 6-by-3 in rectangle. How much carpet is needed?

   Answer. 58 square in

   40 + 18 = 58 square in.

7. 7.

   Luis is painting a triangular sail with base 12 ft and height 10 ft. How much area will the paint cover?

   Answer. 60 square ft

   A = 12 × 12 × 10 = 60 square ft.

8. 8.

   Owen tiles a patio that is a trapezoid with bases 6 cm and 14 cm and height 8 cm. What area of tile is needed?

   Answer. 80 square cm

   A = 12(6 + 14)(8) = 80 square cm.

9. 9.

   Sam’s classroom floor is an L-shape: a 7-by-6 in rectangle joined to a 4-by-3 in rectangle. How much carpet is needed?

   Answer. 54 square in

   42 + 12 = 54 square in.

10. 10.

    Priya is painting a triangular sail with base 5 ft and height 14 ft. How much area will the paint cover?

    Answer. 35 square ft

    A = 12 × 5 × 14 = 35 square ft.

11. 11.

    Think

    Jonah forgot the 12 and computed (7 + 13) × 4 = 80 for the trapezoid. What is the actual area?

    Answer. 40 square in

    Trapezoid area is half of that: 12(7 + 13)(4) = 40 square in.

12. 12.

    Think

    Mei multiplied all four numbers 6×6×4×5 for an L-shaped floor. Split it instead: 6-by-6 joined to 4-by-5. What is the area?

    Answer. 56 square ft

    Add the two rectangles: 36 + 20 = 56.

Original extra practice. Keys are computed from the items, not guessed.