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Geometric Shapes Measurement

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Geometric Shapes Measurement

Talia and Omar are checking measurements for a new theme park. Use angle facts, perimeter, area, and scale to help them. Show working where asked. Diagrams are not drawn to scale.

Angles and polygons

1.At the entrance, two straight paths cross. One angle is 68°. What is the size of the angle directly opposite it? Explain the angle fact you used.

2.A ride platform is a quadrilateral. Three interior angles are 92°, 105° and 78°. Find the fourth interior angle. Show your calculation.

3.A triangular sign has angles of 47° and 63°. Work out the third angle, then classify the triangle by its angles.

4.The park's six-sided welcome sign is a regular hexagon. Use the formula (n − 2) × 180° to find the sum of its interior angles, then find each interior angle.

Measure and compare

5.A rectangular queue area is 18 m long and 7 m wide. Calculate its perimeter and area. Include the correct units.

6.A triangular shade sail has a base of 12 m and a perpendicular height of 5 m. Find its area. Remember that the height must meet the base at a right angle.

7.On a park plan, 1 cm represents 4 m. A path measures 6.5 cm on the plan. What is its actual length?

8.A small model ride has side lengths 3 cm, 4 cm and 5 cm. Its full-size version has corresponding side lengths 9 m, 12 m and 15 m. Are the model and ride similar? State the scale factor from model to full size, using consistent units.

Design and justify

9.Isla is building a triangular sign with two sides of 8 cm and 5 cm and an included angle of 60°. Draw a labelled construction using a ruler and protractor. Then explain how you can check the third side and the other two angles are reasonable.