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10.6.0: Exercises

  • Page ID
    171797
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    For the following exercises, find the area of the figure with the given measurements.

    Exercise \(\PageIndex{1}\)

    Area of a triangle with base equal to 10 cm, and height equal to 15 cm.

    Exercise \(\PageIndex{2}\)

    Area of right triangle with base 54 cm, and height equal to 72 cm.

    Exercise \(\PageIndex{3}\)

    A triangle has an area of \(22.5\,{\text{c}}{{\text{m}}^2}.\) If the base equals 5 cm, find the height.

    Exercise \(\PageIndex{4}\)

    Find the area of the triangle with base equal to 2.5 in, height equal to 0.7 in as shown.

    A triangle with its sides marked 2 inches, 2.5 inches, and 1.5 inches. The height is marked 0.7 inches.

    Exercise \(\PageIndex{5}\)

    Find the area of the trapezoid with \({b_1} = 30\,in,\,\) \({b_2} = 14\,in\), and \(h = 10\,in\) as shown.

    A trapezoid with its top and bottom bases marked 14 inches and 30 inches. The height is marked 10 inches.

    Exercise \(\PageIndex{6}\)

    Find the area of the trapezoid shown.

    A trapezoid with its top and bottom bases marked 5 centimeters and 12 centimeters. The height is marked 12 centimeters.

    Exercise \(\PageIndex{7}\)

    Find the area of a parallelogram with base equal to 50 cm and height equal to 35 cm as shown.

    A parallelogram with its base marked 50 centimeters and height marked 35 centimeters.

    Exercise \(\PageIndex{8}\)

    Find the area of a parallelogram with base equal to 20 in, and height equal to 22 in.

    Exercise \(\PageIndex{9}\)

    Find the area of the rhombus shown.

    A rhombus with two diagonal lines. The lines measure 6 centimeters and 4.5 centimeters.

    Exercise \(\PageIndex{10}\)

    Find the area of the regular pentagon with the apothem equal to 5.5 in and the side length equal to 6 in as shown.

    A pentagon. Each side measures 6 inches. The apothem is marked 5.5 inches.

    Exercise \(\PageIndex{11}\)

    Find the area of the regular octagon with apothem equal to 7 cm and the side length is 3.5 cm as shown.

    An octagon. Each side measures 3.5 centimeters. The apothem is marked 7 centimeters.

    Exercise \(\PageIndex{12}\)

    Find the area of a regular pentagon with apothem equal 1.5 in, and the sides are equal to 3 in as shown.

    A pentagon. Each side measures 3 inches. The apothem is marked 1.5 inches.

    Exercise \(\PageIndex{13}\)

    Find the area of a circle with radius of 3 cm as shown.

    A circle with its radius, r marked 3 centimeters.

    Exercise \(\PageIndex{14}\)

    You are installing a countertop in the shape of a trapezoid with a round sink as shown in the figure. After the sink is installed, how much area is left on the countertop?

    A circle is drawn with a trapezoid. The top and bottom bases of the trapezoid measure 30 inches and 36 inches. The radius of the circle is marked 10 inches. The circle touches the top and bottom bases of the trapezoid. The region outside the circle is shaded.

    Exercise \(\PageIndex{15}\)

    Find the area of the shaded region in the given figure.

    A square is circumscribed about a circle. The radius of the circle is marked 3 feet.

    Exercise \(\PageIndex{16}\)

    You have a structural post in the corner of your kitchen. The adjacent room is the family room and the two rooms are separated by a transparent glass wall. To camouflage the post, you decide to have five shelves built that will fill the corner, as shown in the figure. The rectangular shelves are 26 inches wide and 24 inches deep. The diameter of the post is 6 inches. How much shelf area will be available after the shelves are built around the post? The laminate material for the shelves runs $25 per square foot. How much will the laminate shelves cost?

    An illustration shows a transparent glass wall, five shelves, and cabinets.

    Exercise \(\PageIndex{17}\)

    Find the area of the shaded region in the given figure.

    A rhombus is inscribed in a trapezoid. The top and bottom bases of the trapezoid measure 16 inches and 10 inches. The diagonals of the rhombus measure 13 inches and 12 inches.

    Exercise \(\PageIndex{18}\)

    Find the area of the shaded region in the given figure.

    A circle is inscribed in a triangle. The radius of the circle is 3 inches. The sides of the triangle measure 15 inches. A line is drawn from the bottom-left vertex of the triangle to the midpoint of the right side of the triangle, passing through the circle. This line measures 10 inches.

    Exercise \(\PageIndex{19}\)

    Find the area of the shaded region in the given figure. All measurements in centimeters.

    A triangle is inscribed in a circle. The radius of the circle is marked r equals 5. A vertical dashed line is drawn from the peak of the triangle to meet the base at its center. The height of the triangle is marked h equals 8. The base of the triangle measures 4 on either side of the dashed line.

    Exercise \(\PageIndex{20}\)

    Your property measures 2 miles wide by 2.5 miles long. You want to landscape it but the landscaper charges by the square foot. How many square feet need to be landscaped?

    Exercise \(\PageIndex{21}\)

    Find the area of the window shown.

    A figure shows a semicircle placed on top of a rectangle. The length and width of the rectangle measure 9 feet and 3.2 feet. The diameter of the circle measures 3.2 feet.

    Exercise \(\PageIndex{22}\)

    What is the area of a major league baseball diamond enclosed by the baselines if it forms a square with 90ft between bases?


    10.6.0: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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