Lesson 10.3: Area Of Triangles

1. The area of a parallelogram is twice the area of congruent triangles formed by the parallelogram

False

True

The statement is true because the area of a parallelogram is indeed twice the area of congruent triangles formed by the parallelogram. This is a property of parallelograms, where the base of the triangle is equal to one side of the parallelogram and the height of the triangle is equal to the distance between the base and the opposite side of the parallelogram. Therefore, the area of the parallelogram can be calculated by multiplying the base by the height, which is the same as calculating the area of two congruent triangles and adding them together.

Explanation

The statement is true because the area of a parallelogram is indeed twice the area of congruent triangles formed by the parallelogram. This is a property of parallelograms, where the base of the triangle is equal to one side of the parallelogram and the height of the triangle is equal to the distance between the base and the opposite side of the parallelogram. Therefore, the area of the parallelogram can be calculated by multiplying the base by the height, which is the same as calculating the area of two congruent triangles and adding them together.

2. What is the area of a triangle with base 10 cm and height 25 cm?

35 sq cm

62.5 sq cm

125 sq cm

250 sq cm

The area of a triangle can be calculated using the formula: Area = (base * height) / 2. In this case, the base is given as 10 cm and the height is given as 25 cm. Plugging these values into the formula, we get: Area = (10 * 25) / 2 = 250 / 2 = 125 sq cm.

Explanation

The area of a triangle can be calculated using the formula: Area = (base * height) / 2. In this case, the base is given as 10 cm and the height is given as 25 cm. Plugging these values into the formula, we get: Area = (10 * 25) / 2 = 250 / 2 = 125 sq cm.

3. What is the area of a parallelogram with base 30 ft and height 25 ft?

55 sq ft

187.5 sq ft

375 sq ft

750 sq ft

The area of a parallelogram can be calculated by multiplying the base length by the height. In this case, the base is given as 30 ft and the height is given as 25 ft. Therefore, the area of the parallelogram is 30 ft x 25 ft = 750 sq ft.

Explanation

The area of a parallelogram can be calculated by multiplying the base length by the height. In this case, the base is given as 30 ft and the height is given as 25 ft. Therefore, the area of the parallelogram is 30 ft x 25 ft = 750 sq ft.

4. Find the area of a triangle with base of 4 in and height of 6 in.

12 sq in

24 sq in

12 in

24 in

To find the area of a triangle, we can use the formula A = (1/2) * base * height. In this case, the base is given as 4 inches and the height is given as 6 inches. Plugging these values into the formula, we get A = (1/2) * 4 * 6 = 12 square inches. Therefore, the correct answer is 12 sq in.

Explanation

To find the area of a triangle, we can use the formula A = (1/2) * base * height. In this case, the base is given as 4 inches and the height is given as 6 inches. Plugging these values into the formula, we get A = (1/2) * 4 * 6 = 12 square inches. Therefore, the correct answer is 12 sq in.

5. The base of a triangle with area of 40 cm² and height of 5 cm is _________.

400 sq cm

16 sq cm

8 sq cm

20 cm

The area of a triangle is calculated by multiplying the base length by the height and dividing the result by 2. In this case, the area is given as 40 cm2 and the height is given as 5 cm. By rearranging the formula, we can solve for the base length. Multiplying the height by 2 and then dividing the area by the result gives us the base length of 16 cm. Therefore, the correct answer is 16 sq cm.

Explanation

The area of a triangle is calculated by multiplying the base length by the height and dividing the result by 2. In this case, the area is given as 40 cm2 and the height is given as 5 cm. By rearranging the formula, we can solve for the base length. Multiplying the height by 2 and then dividing the area by the result gives us the base length of 16 cm. Therefore, the correct answer is 16 sq cm.