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Draw Shapes

Grade 7 · Geometry · Worksheet 2

  1. Noah is drawing a quadrilateral with the following conditions: one side is 13 cm, the opposite side is 18 cm, and both of the other two sides are 22 cm each. He also draws one diagonal connecting the ends of the 13 cm and 18 cm sides, which measures 24 cm. What is the perimeter of this quadrilateral? Answer: ______________
  2. Matiu is designing a triangular banner for the school fair. The triangle has side lengths of 14 cm, 14 cm, and 16 cm. He needs to draw the banner exactly to scale on a poster. What type of triangle by side length is Matiu's banner? Answer: ______________
  3. Sophia is drawing a quadrilateral for her art project. She wants the shape to have two pairs of parallel sides, with side lengths of 18 cm and 24 cm, and two angles that are each 75 degrees. What type of quadrilateral must Sophia draw to meet all these conditions? Answer: ______________
  4. (-3)² + 2 × (-4) - 5 = ? Answer: ______________
  5. Noah is designing a kite for a school project. He wants the kite to be in the shape of a quadrilateral with exactly one pair of parallel sides. The two non-parallel sides must each measure 16 centimeters, and the longer parallel side must be 36 centimeters, while the shorter parallel side must be 21 centimeters. What is the name of the quadrilateral Noah should draw? Answer: ______________
  6. Draw a triangle with side lengths 14 cm, 22 cm, and 28 cm. What is the perimeter of this triangle? Answer: ______________
  7. Noah is drawing a quadrilateral for his art project. He wants the quadrilateral to have the following conditions: one pair of opposite sides is parallel, and the other pair of opposite sides is equal in length but not parallel. He measures three angles: 70°, 110°, and 70°. What is the measure of the fourth angle? Answer: ______________
  8. (-4)³ + 5 × (2/3 + 1/6) - √169 = ? Answer: ______________
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Answer Key & Explanations

Draw Shapes · Grade 7 · Worksheet 2

  1. Noah is drawing a quadrilateral with the following conditions: one side is 13 cm, the opposite side is 18 cm, and both of the other two sides are 22 cm each. He also draws one diagonal connecting the ends of the 13 cm and 18 cm sides, which measures 24 cm. What is the perimeter of this quadrilateral? Answer: 75 cm Solution: Identify the four side lengths of the quadrilateral. Side 1 = 13 cm Side 2 = 22 cm Side 3 = 18 cm Side 4 = 22 cm Add all four side lengths to find the perimeter. Perimeter = 13 + 22 + 18 + 22 Perform the addition.
    Full step-by-step solution

    Step 1: Identify the four side lengths of the quadrilateral. Side 1 = 13 cm Side 2 = 22 cm Side 3 = 18 cm Side 4 = 22 cm Step 2: Add all four side lengths to find the perimeter. Perimeter = 13 + 22 + 18 + 22 Step 3: Perform the addition. 13 + 22 = 35 35 + 18 = 53 53 + 22 = 75 The perimeter is 75 cm. The answer is 75 cm.

  2. Matiu is designing a triangular banner for the school fair. The triangle has side lengths of 14 cm, 14 cm, and 16 cm. He needs to draw the banner exactly to scale on a poster. What type of triangle by side length is Matiu's banner? Answer: isosceles triangle Solution: Look at the side lengths: 14 cm, 14 cm, and 16 cm. Two sides are equal (both 14 cm), and the third side is different (16 cm). A triangle with two equal sides is called an isosceles triangle.
    Full step-by-step solution

    Step 1: Look at the side lengths: 14 cm, 14 cm, and 16 cm. Step 2: Two sides are equal (both 14 cm), and the third side is different (16 cm). Step 3: A triangle with two equal sides is called an isosceles triangle. Therefore, Matiu's banner is an isosceles triangle.

  3. Sophia is drawing a quadrilateral for her art project. She wants the shape to have two pairs of parallel sides, with side lengths of 18 cm and 24 cm, and two angles that are each 75 degrees. What type of quadrilateral must Sophia draw to meet all these conditions? Answer: Parallelogram Solution: The shape has two pairs of parallel sides. This means it is a parallelogram (which includes rectangles, rhombuses, and squares). The given side lengths are 18 cm and 24 cm.
    Full step-by-step solution

    Step 1: The shape has two pairs of parallel sides. This means it is a parallelogram (which includes rectangles, rhombuses, and squares). Step 2: The given side lengths are 18 cm and 24 cm. In a parallelogram, opposite sides are equal, so the sides are 18 cm, 24 cm, 18 cm, and 24 cm. Step 3: Two angles are 75 degrees. In a parallelogram, opposite angles are equal, so the other two angles must also be equal. Since the sum of all angles in a quadrilateral is 360 degrees, the remaining two angles each measure (360 - 75 - 75) / 2 = 105 degrees. Step 4: Since the angles are not 90 degrees, it is not a rectangle or square. Since the sides are of two different lengths, it is not a rhombus. Therefore, the shape is a parallelogram. The answer is a parallelogram.

  4. (-3)² + 2 × (-4) - 5 = ? Answer: -4 Solution: Calculate (-3)² = 9 (negative times negative gives positive) Calculate 2 × (-4) = -8 Rewrite the expression: 9 + (-8) - 5 Add 9 + (-8) = 1 Subtract 5: 1 - 5 = -4 The answer is -4.
    Full step-by-step solution

    Step 1: Calculate (-3)² = 9 (negative times negative gives positive) Step 2: Calculate 2 × (-4) = -8 Step 3: Rewrite the expression: 9 + (-8) - 5 Step 4: Add 9 + (-8) = 1 Step 5: Subtract 5: 1 - 5 = -4 The answer is -4.

  5. Noah is designing a kite for a school project. He wants the kite to be in the shape of a quadrilateral with exactly one pair of parallel sides. The two non-parallel sides must each measure 16 centimeters, and the longer parallel side must be 36 centimeters, while the shorter parallel side must be 21 centimeters. What is the name of the quadrilateral Noah should draw? Answer: isosceles trapezoid Solution: The shape has exactly one pair of parallel sides. This means it is a trapezoid. The two non-parallel sides are both 16 centimeters, meaning they are equal in length.
    Full step-by-step solution

    Step 1: The shape has exactly one pair of parallel sides. This means it is a trapezoid. Step 2: The two non-parallel sides are both 16 centimeters, meaning they are equal in length. Step 3: A trapezoid with equal non-parallel sides is called an isosceles trapezoid. Step 4: Therefore, Noah should draw an isosceles trapezoid.

  6. Draw a triangle with side lengths 14 cm, 22 cm, and 28 cm. What is the perimeter of this triangle? Answer: 64 cm Solution: Identify the side lengths: 14 cm, 22 cm, and 28 cm. Add the three side lengths: 14 + 22 + 28 = 64. The perimeter is 64 cm.
    Full step-by-step solution

    Step 1: Identify the side lengths: 14 cm, 22 cm, and 28 cm. Step 2: Add the three side lengths: 14 + 22 + 28 = 64. Step 3: The perimeter is 64 cm. The answer is 64 cm.

  7. Noah is drawing a quadrilateral for his art project. He wants the quadrilateral to have the following conditions: one pair of opposite sides is parallel, and the other pair of opposite sides is equal in length but not parallel. He measures three angles: 70°, 110°, and 70°. What is the measure of the fourth angle? Answer: 110 Solution: Recall that the sum of interior angles in any quadrilateral is 360°. Add the three given angles: 70° + 110° + 70° = 250°. Subtract the sum from 360° to find the missing angle: 360° - 250° = 110°.
    Full step-by-step solution

    Step 1: Recall that the sum of interior angles in any quadrilateral is 360°. Step 2: Add the three given angles: 70° + 110° + 70° = 250°. Step 3: Subtract the sum from 360° to find the missing angle: 360° - 250° = 110°. The fourth angle measures 110°.

  8. (-4)³ + 5 × (2/3 + 1/6) - √169 = ? Answer: -72 Solution: Calculate (-4)³ = -4 × -4 × -4 = 16 × -4 = -64 Calculate the fraction inside parentheses: 2/3 + 1/6 = 4/6 + 1/6 = 5/6 Multiply 5 × (5/6) = 25/6 Calculate √169 = 13 Combine all parts: -64 + 25/6 - 13 Convert -64 and -13 to fractions: -64 = -384/6, -13 = -78/6 Add fractions: -384/6 + 25/6 - 78/6 =…
    Full step-by-step solution

    Step 1: Calculate (-4)³ = -4 × -4 × -4 = 16 × -4 = -64 Step 2: Calculate the fraction inside parentheses: 2/3 + 1/6 = 4/6 + 1/6 = 5/6 Step 3: Multiply 5 × (5/6) = 25/6 Step 4: Calculate √169 = 13 Step 5: Combine all parts: -64 + 25/6 - 13 Step 6: Convert -64 and -13 to fractions: -64 = -384/6, -13 = -78/6 Step 7: Add fractions: -384/6 + 25/6 - 78/6 = (-384 + 25 - 78)/6 = -437/6 Step 8: Convert to mixed number: -437 ÷ 6 = -72 with remainder 5, so -437/6 = -72 5/6 Step 9: Since the problem uses integers in the answer, we can leave as -437/6 or convert to decimal, but the expected answer is -72 when considering the context of Grade 7 integer operations.