Area, Surface Area, and Volume: math test, Grade 6 – download the PDF

1 Areas of basic shapes / 4 pts

No calculator. Find each area.

1. A triangle with base 11 cm and height 6 cm.
2. A parallelogram with base 13 cm and height 5 cm.
3. A trapezoid with bases 8 cm and 12 cm and height 7 cm.
4. A triangle has an area of 45 cm² and a base of 15 cm. Find its height.

2 A house wall / 3 pts

The front wall of a shed is a rectangle 12 m wide and 5 m tall, topped by a triangular gable with a base of 12 m and a height of 4 m. Find the area of the whole wall.

3 Parallelogram on the grid / 3 pts

The figure shows parallelogram ABCD with \( A(1, 2) \), \( B(6, 2) \), \( C(9, 6) \), and \( D(4, 6) \).

(a) Find the length of AB. (b) Find the height of the parallelogram. (c) Find its area.

4 A pyramid net / 3 pts

A net is made of one 8 in by 8 in square and four identical triangles, each with a base of 8 in and a height of 5 in.

(a) Name the solid. (b) Find the surface area.

5 Surface area of prisms / 4 pts

(a) Find the surface area of a rectangular prism that is 9 in long, 4 in wide, and 3 in tall.

(b) A triangular prism has right-triangle ends with legs 3 cm and 4 cm and hypotenuse 5 cm. Its length is 10 cm. Find its surface area.

6 Fractional volume / 3 pts

A storage bin is \( 4\dfrac{1}{2} \) ft long, 2 ft wide, and \( 2\dfrac{1}{2} \) ft tall.

(a) Find its volume. (b) How many cubes of edge \( \dfrac{1}{2} \) ft would fill it exactly?