Question

Unit 1 lesson 10 base and heights of triangle

Answer 1

All the triangles that have an area of 8 square units include:

1. triangle A.
2. triangle B.
3. triangle D.
4. triangle E.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

• b represent the base area.
• h represent the height.

Note: Each interval on the grid represents 1 unit.

For triangle A, we have:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 4 × 4

Area of triangle = 8 square units.

For triangle B, we have:

Area of triangle = 1/2 × 4 × 4

Area of triangle = 8 square units.

For triangle C, we have:

Area of triangle = 1/2 × 3 × 5

Area of triangle = 7.5 square units.

For triangle D, we have:

Area of triangle = 1/2 × 4 × 4

Area of triangle = 8 square units.

For triangle E, we have:

Area of triangle = 1/2 × 8 × 2

Area of triangle = 8 square units.

Complete Question:

Select all triangles that have an area of 8 square units. Explain how you know.

Answer 2

Formula to find the area of a triangle =
`(1)/(2)` × base × height

For triangles A, B and D, the base occupies 4 squares and the height occupies 4 squares.

Therefore, area =
`(1)/(2)` × 4 × 4

= 2 × 4 = 8 sq. units

For triangle E, base occupies 2 squares and height occupies 8 squares.

Therefore, area =
`(1)/(2)` × 2 × 8

= 8 sq. units

For triangle C, base occupies 3 squares and height occupies 5 squares.

Therefore, area =
`(1)/(2)` × 3 × 5

= 7.5 sq. units

Hence, triangles whose area is 8 sq. units are A, B, D and E.