Understanding Properties of Triangles Review

Oliver, Zoe, and Priya are working on a project to build a model of a pyramid. They decide to start by calculating the area of one of the triangular faces. If the base of the triangle is 6 cm and the height is 8 cm, what is the area of the triangle?

• 14 cm²

• 30 cm²

• 10 cm²

• 24 cm²

James, Grace, and Isla are working on a project to build a model of a pyramid. They decide to make a triangular base for the pyramid with sides of length 5 cm, 12 cm, and 13 cm. Can you help them find the area of this triangle using Heron's formula?

• 30 cm^2

• 20 cm^2

• 25 cm^2

• 60 cm^2

Abigail, Emma, and Liam are building a model of a right-angled triangle. They have two legs of the triangle with lengths 3 cm and 4 cm. Can you help them figure out the length of the hypotenuse?

• 2 cm

• 10 cm

• 5 cm

• 7 cm

Liam, Maya, and David are building a model of a triangle with sticks. They have sticks of lengths 7 cm, 10 cm, and 15 cm. Can they form a valid triangle with these sticks? Why or why not?

• Yes

• No, because the sum of the two shorter sticks is equal to the longest stick

• No, because the sum of the two shorter sticks is greater than the longest stick

• No, because the sum of the two shorter sticks is not greater than the longest stick

Luna, Avery, and Michael are building a triangular treehouse. If angle B, where Avery is working, measures 45° and angle C, where Michael is working, measures 60°, what is the measure of angle A where Luna is working?

• 75°

• 105°

• 30°

• 90°

Nora, Maya, and Ava are trying to figure out the angle of a missing piece in a triangular puzzle. They know that one angle is 40° and another is 70°. Can you help them find out the measure of the third angle?

• 40°

• 90°

• 110°

• 70°

Aria, Arjun, and Mia are trying to build a triangular tent with sticks of lengths 4, 7, and 10. Can they successfully build the tent?

• Only if one stick's length is doubled

• No

• Maybe

• Yes

David, Isla, and Harper are building a kite. They decide to make the kite in the shape of a triangle. They have a string of 5 cm to connect the kite to the handle. If they make an angle of 30° at the point where the string is attached, what would be the length of the hypotenuse of the triangle (the kite's string) using the sine ratio?

• 15 cm

• 7 cm

• 3 cm

• 10 cm

Nora, Elijah, and Noah are trying to fly a kite. They notice that the string attached to the kite forms a right-angled triangle with the ground. If the sin(θ) of the angle between the string and the ground is 3/5, what is the value of cos(θ)?

• 2/3

• 5/3

• 4/5

• 1/2

Michael is helping Abigail with her math homework. They come across a problem where they have a triangle and the tangent of an angle (θ) is given as 4/3. Jackson, who is also there, challenges them to find the value of sin(θ). Can you help them?

• 5/3

• 2/3

• 3/5

• 4/3