Level 3 · Challenge ← Back to lesson

Area from Rectangles to Triangles: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A triangle has base $(2x+3)$ cm, perpendicular height 5 cm, and area $47.5\text{ cm}^2$ . What is $x$ ?

Answer choices for question 1 A $4$ B $9.5$ C $16$ D $8$
2

A right triangle has legs 20 cm and 21 cm, and hypotenuse 29 cm. What is the altitude to the hypotenuse?

Answer choices for question 2 A $\tfrac{210}{29}$ cm B $\tfrac{420}{29}$ cm C $\tfrac{29}{2}$ cm D $\tfrac{840}{29}$ cm
3

Triangle ABC has base AB of length 7 cm. Its altitude CH meets the extension beyond B, with BH of length 9 cm and CH of length 12 cm. Which calculation gives the triangle area?

Answer choices for question 3 A $\tfrac12\cdot16\cdot12$ B $\tfrac12\cdot9\cdot12$ C $\tfrac12\cdot7\cdot12$ D $7\cdot12$
4

A triangle has sides 10 cm, 17 cm, and 21 cm. Its perpendicular height to the 21 cm side is 8 cm. Which list gives the heights to the 10 cm, 17 cm, and 21 cm sides, in that order?

Answer choices for question 4 A
$\tfrac{84}{5}$ cm

$\tfrac{168}{17}$ cm

$8$ cm
B
$\tfrac{42}{5}$ cm

$\tfrac{84}{17}$ cm

$4$ cm
C
$8$ cm

$\tfrac{168}{17}$ cm

$\tfrac{84}{5}$ cm
D
$10$ cm

$17$ cm

$21$ cm
5

A parallelogram has base 4 units and sideways shift 17 units from bottom to top. It is split into equal-height strips parallel to the base. What is the smallest number of strips that makes each strip shift at most 4 units?

Answer choices for question 5 A $4$ B $8$ C $5$ D $17$
6

A unit square is divided into 25 congruent squares of side $\tfrac15$ unit. A rectangle contains 9 columns and 7 rows of these tiles. What is the rectangle area?

Answer choices for question 6 A $\tfrac{63}{5}$ square units B $\tfrac{63}{25}$ square units C $\tfrac{16}{25}$ square unit D $\tfrac{63}{10}$ square units
7

Which describes the status of the rectangle formula for irrational side lengths in this lesson?

Answer choices for question 7 A It is accepted as an extension of the formula proved by finite rational tiling B It follows because every irrational side is exactly a finite sum of rational grid steps C It is false whenever either side is irrational D It follows from preserving the rectangle perimeter
8

A right triangle has positive leg lengths $x$ cm and $(x+7)$ cm, and area $60\text{ cm}^2$ . What is its perimeter?

Answer choices for question 8 A $23$ cm B $30$ cm C $46$ cm D $40$ cm
9

A rectangle has positive side lengths $(2+\sqrt3)$ cm and $(2-\sqrt3)$ cm. What is its exact area?

Answer choices for question 9 A $4\text{ cm}^2$ B $1\text{ cm}^2$ C $7\text{ cm}^2$ D $4\sqrt3\text{ cm}^2$
10

An isosceles triangle has sides 13 cm, 13 cm, and 10 cm. What is its area?

Answer choices for question 10 A $65\text{ cm}^2$ B $120\text{ cm}^2$ C $30\text{ cm}^2$ D $60\text{ cm}^2$
11

A triangle has a 10 cm side with matching height 6 cm. A second side has length 13 cm. What height matches the second side?

Answer choices for question 11 A $\tfrac{60}{13}$ cm B $\tfrac{30}{13}$ cm C $\tfrac{13}{6}$ cm D $\tfrac{78}{10}$ cm
12

Two congruent triangles fill a parallelogram with base 20 units and area 140 square units. One triangle uses the same base and height as the parallelogram. What is that triangle height?

Answer choices for question 12 A $3.5$ units B $14$ units C $7$ units D $70$ units

← Back to lesson