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Home > CC2 > Chapter 5 > Lesson 5.2.6 > Problem 5-84

5-84.

Manuel used pattern blocks to build the shapes below. The block marked A is a square, B is a trapezoid, C is a rhombus (a parallelogram with equal sides), and D is a triangle. Find the area of each of Manuel’s shapes.

  1. A trapezoid, labeled B, with horizontal parallel sides and a square, labeled A, shares its bottom side with the top side of the trapezoid. A, has 3 angles labeled as right, with top and right sides, labeled 2.5 centimeters. Bottom parallel side, on B, labeled, 5 centimeters. A dashed line, connecting the two parallel sides, at a right angle, labeled 2 cm.

  1. A rhombus, labeled C, and a triangle labeled D. The base of the triangle, and the top side of the rhombus, share a side. Labeled on C: bottom and right side, each 2.5 cm. Dashed line on C, connecting the top and bottom sides at right angles, labeled 2 centimeters. Labeled on D, right side, 2.5 cm, and a dashed line, From the top vertex, perpendicular to the base, 2.2 centimeters.

Examine each complex shape in terms of each individual shape within the entire structure and add up the areas to get the total area of Manuel's shapes.

  1. Shading added to same figure, A in blue, and B in brown.

    Make sure to remember formulas for calculating area:
    Square: 

    Trapezoid: 

    Triangle: 

    square cm

    Be sure to know why this is the answer from the given measurements.
    Now try solving for part (b).

  1. Shading added to same figure, D in green, and C in red.

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