Testinar Grade 6 math

Area of Triangles

Students will build Grade 6 mastery of area of triangles using models, equations, and test-style reasoning.

CH04-01 Geometry
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. What is the area of a triangle with base \(10\) cm and height \(6\) cm?

    Area of Triangles visual for G6-C04-T01-Q001
    1. \(16\) cm\(^2\)
    2. \(30\) cm\(^2\)
    3. \(60\) cm\(^2\)
    4. \(120\) cm\(^2\)

  2. A triangle has a base of \(8\) inches and a height of \(4\) inches. What is its area?

    Area of Triangles visual for G6-C04-T01-Q002
    1. \(12\) in\(^2\)
    2. \(64\) in\(^2\)
    3. \(32\) in\(^2\)
    4. \(16\) in\(^2\)

  3. Which formula correctly finds the area of a triangle?

    1. \(A=b+h\)
    2. \(A=2bh\)
    3. \(A=\frac{1}{2}bh\)
    4. \(A=bh\)

  4. A right triangle has legs of length \(5\) m and \(12\) m. What is its area?

    Area of Triangles visual for G6-C04-T01-Q004
    1. \(17\) m\(^2\)
    2. \(30\) m\(^2\)
    3. \(60\) m\(^2\)
    4. \(120\) m\(^2\)

  5. An isosceles triangle has a base of \(14\) cm. A perpendicular line from the top vertex to the base has length \(9\) cm. What is the area?

    Area of Triangles visual for G6-C04-T01-Q005
    1. \(23\) cm\(^2\)
    2. \(28\) cm\(^2\)
    3. \(56\) cm\(^2\)
    4. \(63\) cm\(^2\)

  6. What is the height of a triangle with area \(24\) ft\(^2\) and base \(8\) ft?

    1. \(3\) ft
    2. \(6\) ft
    3. \(16\) ft
    4. \(32\) ft

  7. Find the base of a triangle with area \(45\) m\(^2\) and height \(10\) m.

    1. \(4.5\) m
    2. \(90\) m
    3. \(18\) m
    4. \(9\) m

  8. Identify the height in the triangle shown. The height must be perpendicular to the base.

    Area of Triangles visual for G6-C04-T01-Q009
    1. \(10\) cm
    2. \(7.5\) cm
    3. \(7\) cm
    4. \(3.5\) cm
Teacher and parent reference

Answer key and explanations

  1. B. \(30\) cm\(^2\)

    Area of a triangle \(=\frac{1}{2}\times b\times h=\frac{1}{2}\times10\times6=30\) cm\(^2\).

  2. D. \(16\) in\(^2\)

    Using \(A=\frac{1}{2}bh\), we get \(A=\frac{1}{2}\times 8\times 4=16\) in\(^2\).

  3. C. \(A=\frac{1}{2}bh\)

    The area formula for any triangle is \(A=\frac{1}{2}bh\), where \(b\) is base and \(h\) is height.

  4. B. \(30\) m\(^2\)

    For a right triangle, \(A=\frac{1}{2}\times 5\times 12=30\) m\(^2\).

  5. D. \(63\) cm\(^2\)

    \(A=\frac{1}{2}\times 14\times 9=63\) cm\(^2\).

  6. B. \(6\) ft

    Rearranging \(A=\frac{1}{2}bh\): \(24=\frac{1}{2}\times 8\times h \Rightarrow h=6\) ft.

  7. D. \(9\) m

    Solving \(45=\frac{1}{2}\times b\times 10 \Rightarrow b=9\) m.

  8. C. \(7\) cm

    The height is the perpendicular distance from the base to the opposite vertex, shown by the dashed line as \(7\) cm.

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